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In the present paper corrected versions of the statements in the paper "Description of finite-dimensional inner Rickart and Baer Jordan algebras" by F.N. Arzikulov and U.I. Khakimov are given. In particular, it is shown that for any Jordan algebra J with an idempotent p and an associative degenerate radical D such that J = F p + ̇ D , J is an inner RJ-algebra if and only if, for any nonzero a ∈ D , a 2 = 0 and p(pa) = pa. Also, other equivalent conditions when a Jordan algebra J is an inner RJ-algebra are given. As for finite-dimensional nilpotent Jordan algebras, there is not a nilpotent inner RJ-algebra (and hence inner BJ-algebra) except the finite-dimensional Jordan algebra the square of each element of which is zero. [ABSTRACT FROM AUTHOR]

In a previous paper we have compared the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two idempotents. In the present paper, we compare the Hochschild cohomology groups of finite dimensional monomial algebras under gluing two arrows. [ABSTRACT FROM AUTHOR]

This work is devoted to the complete classification of solvable Leibniz algebras with the naturally graded quasi-filiform non-Lie nilradical. It should be noted that the class of naturally graded quasi-filiform Leibniz algebras is sufficiently large, and solvable Leibniz algebras with the nilradical which is isomorphic to several of these algebras are classified in a series of works. This paper considered all omitted cases and completed the problem of classifying solvable Leibniz algebras with naturally graded quasi-filiform non-Lie nilradical. At the end of the paper we combine all results obtained to date, and provide a complete list of solvable Leibniz algebras, whose nilradical is a naturally graded quasi-filiform Leibniz algebra. [ABSTRACT FROM AUTHOR]

Köthe's classical problem posed by G. Köthe in 1935 asks to describe the rings R such that every left R-module is a direct sum of cyclic modules (these rings are known as left Köthe rings). Köthe, Cohen and Kaplansky solved this problem for all commutative rings (that are Artinian principal ideal rings). During the years 1962 to 1965, Kawada solved Köthe's problem for basic finite-dimensional algebras. But, so far, Köthe's problem was open in the non-commutative setting. Recently, in the paper [Several characterizations of left Köthe rings, Rev. Real Acad. Cienc. Exactas Fis. Nat. Ser. A-Mat. (2023) (to appear)]], we classified left Köthe rings into three classes one contained in the other: left Köthe rings, strongly left Köthe rings and very strongly left Köthe rings, and then, we solved Köthe's problem by giving several characterizations of these rings in terms of describing the indecomposable modules. In this paper, we will introduce the Morita duals of these notions as left co-Köthe rings, strongly left co-Köthe rings and very strongly left co-Köthe rings, and then, we give several structural characterizations for each of them. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, Wolbachia infection in a bisexual and diploid population with a fixed cytoplasmic incompatibility rate w and maternal transmission rate d is studied as an evolution algebra. As the cytoplasmic incompatibility (CI) of the population causes deaths in the offspring, the evolution algebra of this model is not baric, and is a dibaric algebra if and only if the cytoplasmic incompatibility rate w is 1 and d=1 . The idempotent elements are given in terms of d and w. Moreover, this algebra has no absolute nilpotent elements when CI expression w≠1 . [ABSTRACT FROM AUTHOR]

AbstractLet R be a commutative ring with identity and R′ be the integral closure of R. In this paper, we show that if R is an affine algebra over a field K, then every regular ideal of R′ is finitely generated, i.e., R′ is an r-Noetherian ring. We also study when the integral closure of an affine algebra is Noetherian. First we show that if R is a Krull ring such that R/P is a Noetherian domain for each minimal regular prime ideal P of R, then R is an r-Noetherian ring, which is a generalization of Nishimura’s result. As an application of this result, we prove that if R is an r-Noetherian ring with reg-dim R≤2 , then R′ is an r-Noetherian ring. We finally construct a couple of r-Noetherian rings, e.g., an r-Noetherian ring R that is not Noetherian and reg-dim R=∞ or reg-dim R=n≤ dim R=n+m−1 for arbitrary positive integers n, m. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we generalize the classical method used to classify nilpotent low-dimensional Lie algebras to serve for nilpotent Bol algebras. The algebraic classification of the nilpotent Bol algebras up to dimension four is given. [ABSTRACT FROM AUTHOR]

Let (X , ≤) be a locally finite pre-ordered set and R be a commutative ring with unity. In this paper we apply the theory of zero product determined algebras to show that each linear map on the incidence algebra I (X , R) which is derivable at zero is a generalized derivation and every local derivation on I (X , R) is a derivation. [ABSTRACT FROM AUTHOR]

Since the existing tropical cryptographic protocols are either susceptible to the Kotov-Ushakov attack and its generalization, or to attacks based on tropical matrix periodicity and predictive behavior, several attempts have been made to propose protocols that resist such attacks. Despite these attempts, many of the proposed protocols remain vulnerable to attacks targeting the underlying hidden problems, one of which we call the tropical two-sided discrete logarithm with shift. An illustrative case is the tropical Stickel protocol, which, when formulated with a single monomial instead of a polynomial, becomes susceptible to attacks based on solutions of the above mentioned tropical version of discrete logarithm. In this paper we will formally introduce the tropical two-sided discrete logarithm with shift, discuss how it is solved, and subsequently demonstrate an attack on a key exchange protocol based on the tropical semiring of pairs. This particular protocol is compromised due to the existence of efficient (albeit heuristic) solution of the tropical two-sided logarithm problem, and this highlights the ongoing challenges in search of a "good" key exchange protocol in tropical cryptography. [ABSTRACT FROM AUTHOR]

In this paper, Whittaker modules are studied for a subalgebra q ϵ of the N =2 superconformal algebra. The Whittaker modules are classified by central characters. Additionally, criteria for the irreducibility of the Whittaker modules are given. [ABSTRACT FROM AUTHOR]

Let A be an associative superalgebra endowed with a pseudoautomorphism p. In this paper we generalize the Wedderburn-Malcev Theorem in this setting and we prove that the sequence of p-codimensions of A is polynomially bounded if and only if the variety generated by A does not contain the group algebra of Z 2 and the algebra of 2 × 2 upper-triangular matrices with suitable pseudoautomorphisms. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, all biderivations of solvable Lie algebras of maximal rank g=Q⊕N are characterized. Namely, we consider a solvable Lie algebra of the form g=Q⊕N , where Q is the maximal torus subalgebra of g, N is the nilradical of g and dimQ=dimN/N2 .In the case dimQ=N we characterize the form of skew-symmetric and symmetric biderivations of g . As applications, the forms of linear commuting (skew-commuting) maps and the commutative post-Lie algebra structures on g are given. [ABSTRACT FROM AUTHOR]

AbstractThis paper starts by showing that, for algebras in a certain class, the concepts of weak nilpotency and nilpotency coincide. It goes on to describe some solvability and nilpotency properties of bicommutative algebras, of assosymmetric algebras and of Novikov algebras and to introduce a Frattini theory for all of them. A description is also given for semisimple bicommutative algebras over any field. [ABSTRACT FROM AUTHOR]

AbstractLet k be an arbitrary field and let b>1,n>1 and a be three positive integers. In this paper we explicitly describe a minimal S-graded free resolution of the semigroup algebra k[S] when S is a generalized repunit numerical semigroup, that is, when S is the submonoid of N generated by {a1,a2,…,an} where a1=∑j=0n−1bj and ai−ai−1=a bi−2, i=2,…,n, with gcd(a,a1)=1. [ABSTRACT FROM AUTHOR]

In this paper, we first investigate some properties of relative Rota-Baxter operators on Leibniz conformal algebras with respect to representations and their connections with Leibniz dendriform conformal algebras. Next, we introduce the notion of a twisted relative Rota-Baxter operator and construct a conformal NS-Leibniz algebra structure related to twisted relative Rota-Baxter operators. Furthermore, we define the cohomology of a twisted relative Rota-Baxter operator with coefficients in a suitable representation. Finally, we consider formal deformations of twisted relative Rota-Baxter operators from cohomological points of view. [ABSTRACT FROM AUTHOR]

Let D be an F-central division algebra. In this paper, we investigated the exponent of the group G (D) = D * / Nrd D (D *) D ′ , where D * is the group of units of D, Nrd D (D *) is the image of D * under the reduced norm map and D ′ is the commutator subgroup of D * . We show that if exp (G (D)) < ind (D) , then D and F satisfy strong conditions. In particular, we observe that if D is a sum cyclic algebras in Br (F) , then exp (G (D)) < ind (D) if and only if F is euclidean and D is a tensor product of an ordinary quaternion algebra and a division algebra of odd index. [ABSTRACT FROM AUTHOR]

In this paper, we show that higher Hochschild homology groups do not vanish for a class of Hochschild extension algebras of truncated quiver algebras by the standard duality module. Consequently, this result extends the result of the trivial extension algebra by the standard duality module for truncated quiver algebras. Moreover, as an application, we show that for any Hochschild extension algebra of selfinjective Nakayama algebras by the standard duality module, its Hochschild homology dimension is infinite. [ABSTRACT FROM AUTHOR]

In this paper we study the isotopism classes of two-step nilpotent algebras. We show that every nilpotent Leibniz algebra g with dim [ g , g ] = 1 is isotopic to the Heisenberg Lie algebra or to the Heisenberg algebra l 2 n + 1 J 1 , where J1 is the n × n Jordan block of eigenvalue 1. We also prove that two such algebras are isotopic if and only if the Lie racks integrating them are isotopic. This gives the classification of Lie racks whose tangent space at the unit element is a nilpotent Leibniz algebra with one-dimensional commutator ideal. Eventually, we introduce new isotopism invariants for Leibniz algebras and Lie racks. [ABSTRACT FROM AUTHOR]

Motivated by recent work on compatible mock-Lie algebras such that any linear combination of the two mock-Lie structures is a mock-Lie structure, in this paper we introduce compatible mock-Lie bialgebras as an analogue of compatible Lie bialgebras. They can also be regarded as a "compatible version" of mock-Lie bialgebras. Constructions of compatible mock-Lie bialgebras are presented via Manin triples and matched pairs. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we use the Balinsky-Novikov construction to naturally realize the super Heisenberg-Virasoro algebra g . We then proceed to compute the second cohomology of g with trivial coefficients and determine its universal central extension. This yields two odd 2-cocycles in addition to the Virasoro 2-cocycle. We also calculate the first cohomology group of g in the adjoint module to classify all derivations of g . Finally, we classify all automorphisms of g and describe its automorphism group. [ABSTRACT FROM AUTHOR]

AbstractThis paper is concerned with generalizing the results for Lie CT-algebras to Leibniz algebras. In some cases our results give a generalization even for the case of a Lie algebra. Results on A-algebras are used to show every Leibniz CT-algebra over an algebraically closed field of characteristic different from 2,3 is solvable or is isomorphic to sl2(F). A characterization is then given for solvable Leibniz CT-algebras. It is also shown that the class of solvable Leibniz CT-algebras is factor closed. [ABSTRACT FROM AUTHOR]

AbstractLeibniz algebras are certain generalizations of Lie algebras. Motivated by the concept of subinvariance and ascendancy in group theory, Schenkman studied properties of subinvariant subalgebras of a Lie algebra. Kawamoto studied ascendency in Lie algebras. In this paper we define subinvariance and asendency in Leibniz algebras and study their properties. It is shown that the signature results on subinvariance and ascendency in Lie algebras have analogs for Leibniz algebras. [ABSTRACT FROM AUTHOR]

AbstractIn this paper, we introduce a combinatorial path model of representation of the quantum affine algebra of type Dn, inspired by Mukhin and Young’s combinatorial path models of representations of the quantum affine algebras of types An and Bn. In particular, we give a combinatorial formula for q-characters of fundamental modules of type Dn by assigning each path to a monomial or binomial. By counting our paths, a new expression on dimensions of fundamental modules of type Dn is obtained. [ABSTRACT FROM AUTHOR]

In this paper, first we give the controlling algebra of Lie triple systems. In particular, the cohomology of Lie triple systems can be characterized by the controlling algebra. Then using controlling algebras, we introduce the notions of homotopy Nambu algebras and homotopy Lie triple systems. We show that 2-term homotopy Lie triple systems is equivalent to Lie triple 2-systems, and the latter is the categorification of a Lie triple system. Finally we study skeletal and strict Lie triple 2-systems. We show that skeletal Lie triple 2-systems can be classified the third cohomology group, and strict Lie triple 2-systems are equivalent to crossed modules of Lie triple systems. [ABSTRACT FROM AUTHOR]

The notion of pre-Leibniz algebras was recently introduced in the study of Rota-Baxter operators on Leibniz algebras. In this paper, we first construct a graded Lie algebra whose Maurer-Cartan elements are pre-Leibniz algebras. Using this characterization, we define the cohomology of a pre-Leibniz algebra with coefficients in a representation. This cohomology is shown to split the Loday-Pirashvili cohomology of Leibniz algebras. As applications of our cohomology, we study formal and finite order deformations of a pre-Leibniz algebra. Finally, we define homotopy pre-Leibniz algebras and classify some special types of homotopy pre-Leibniz algebras. [ABSTRACT FROM AUTHOR]

This paper is a first step toward the full description of a family of Hopf algebras whose coradical is isomorphic to a semisimple Hopf algebra Kn, n an odd positive integer, obtained by a cocentral abelian cleft extension. We describe the simple Yetter-Drinfeld modules, compute the fusion rules and determine the finite-dimensional Nichols algebras for some of them. In particular, we give the description of the finite-dimensional Nichols algebras over simple modules over K3. This includes a family of 12-dimensional Nichols algebras { B ξ } depending on 3rd roots of unity. Here, B 1 is isomorphic to the well-known Fomin-Kirillov algebra, and B ξ ≃ B ξ 2 as graded algebras but B 1 is not isomorphic to B ξ as algebra for ξ ≠ 1 . As a byproduct we obtain new Hopf algebras of dimension 216. [ABSTRACT FROM AUTHOR]

The present paper is devoted to the description of local derivations on solvable Lie algebras of maximal rank. Namely, we consider a solvable Lie algebra of the form R = Q ⊕ N , where Q is the maximal torus subalgebra of R , N is the nilradical of R and dim Q = dim N / N 2. We prove that any local derivation of such solvable Lie algebra R is a derivation. Further, we present two examples of solvable Lie algebras which satisfy the condition dim Q < dim N / N 2 and the first algebra admit a local derivation which is not a derivation, while for the second algebra we prove that any local derivation is a derivation. We also apply the main result of the paper to the description of local derivations on so-called standard Borel subalgebras of complex simple Lie algebras. [ABSTRACT FROM AUTHOR]

Let B be a Lie algebra of Block type with basis { L m , i ∣ m , i ∈ Z , i ≥ 0 } and relations [ L m , i , L n , j ] = (n (i + 1) − m (j + 1)) L m + n , i + j . In the present paper, the biderivations of B are explicitly described. In particular, it is shown that any biderivation of B is inner. As applications, the linear commuting maps and commutative post-Lie algebra structures on this algebra are given. [ABSTRACT FROM AUTHOR]

In this paper, we consider a special class of Capelli bitableaux, namely the Capelli bitableaux of the form K λ = [ D e r λ * | D e r λ ] ∈ U (g l (n)) . The main results we prove are the hook coefficient lemma and the expansion theorem. Capelli-Deruyts bitableaux K n p of rectangular shape are of particular interest since they are central elements in the enveloping algebra U (g l (n)) . The expansion theorem implies that the central element K n p is explicitely described as a polynomial in the classical Capelli central elements H n (j) . The hook coefficient lemma implies that the Capelli-Deruyts bitableaux K n p are (canonically) expressed as the products of column determinants. [ABSTRACT FROM AUTHOR]

Let K be a field, [ n ] = { 1 , ... , n } and H = ([ n ] , E) be a hypergraph. For an integer d ≥ 1 the Lovász-Saks-Schrijver ideal (LSS-ideal) L H K (d) ⊆ K [ y i j : (i , j) ∈ [ n ] × [ d ] ] is the ideal generated by the polynomials f e (d) = ∑ j = 1 d ∏ i ∈ e y i j for edges e of H. In this paper for an algebraically closed field K and a k-uniform hypergraph H = ([ n ] , E) we employ a connection between LSS-ideals and coordinate sections of the closure of the set S n , k d of homogeneous degree k symmetric tensors in n variables of rank ≤ d to derive results on the irreducibility of its coordinate sections. To this end we provide results on primality and the complete intersection property of L H K (d) . We then use the combinatorial concept of positive matching decomposition of a hypergraph H to provide bounds on when L H K (d) turns prime to provide results on the irreducibility of coordinate sections of S n , k d . [ABSTRACT FROM AUTHOR]

We continue the study of prime simple modules for quantum affine algebras from the perspective of q-fatorization graphs. In this paper we establish several properties related to simple modules whose q-factorization graphs are afforded by trees. The two most important of them are proved for type A. The first completes the classification of the prime simple modules with three q-factors by giving a precise criterion for the primality of a 3-vertex line which is not totally ordered. Using a very special case of this criterion, we then show that a simple module whose q-factorization graph is afforded by an arbitrary tree is real. Indeed, the proof of the latter works for all types, provided the aforementioned special case is settled in general. [ABSTRACT FROM AUTHOR]

The Lie algebra e 7 1 2 comes from P. Deligne's work on the exceptional series of Lie groups. Using the triality algebra, J. Landsberg and L. Manivel construct this Lie algebra in 2006. In this paper, we study the structure of e 7 1 2 following B. Gross and N. Wallach's work on the highest root and Heisenberg parabolic subalgebra. The process of removing the lowest root from the extended Dynkin diagram of E 8 will contribute to the components of e 7 1 2 . We also study the branching rule of e 7 1 2 to s l (3 , C) and g 2 . We use the computer algebra system SageMath to carry out the branching rule calculations. Then we calculate the Dynkin indices for e 7 1 2 . We find that the number 24 behaves like the 'dual Coxeter number' of e 7 1 2 . [ABSTRACT FROM AUTHOR]

In this paper, we study polynomial identities with involution of an incidence algebra I(P, F) where P is a connected finite poset with an involution λ and F is a field of characteristic zero. At first, we also consider P of length at most 2 and then of length at most 3. Let λ ̂ and σ λ denote, respectively, the λ-orthogonal and the λ-symplectic involutions of I(P, F). For the case that P has length at most 2 and | P | ≥ 4 , we show that the λ ̂ -identities and the σ λ -identities of I(P, F) follow from the ordinary identity [ x 1 , x 2 ] [ x 3 , x 4 ] . In that context, passing to the particular case I (C 2 n , F) , where C 2 n is a poset called crown with 2n elements, and using the classification of the involutions on I (C 2 n , F) , we show that, for all involutions ρ on I (C 2 n , F) , every ρ-identity also follows from the ordinary identity [ x 1 , x 2 ] [ x 3 , x 4 ] . For the case that P has length at most 3 and | P | ≥ 4 , we determine the generators of the T (λ ̂) -ideal I d λ ̂ (I (P , F)) when every element of P that is neither minimal nor maximal is fixed by λ and, for such an element, there exists a unique minimal element of P that is comparable with it. Communicated by Igor Klep [ABSTRACT FROM AUTHOR]

An atomic monoid M is called length-factorial if for every non-invertible element x ∈ M , no two distinct factorizations of x into irreducibles have the same length (i.e., number of irreducible factors, counting repetitions). The notion of length-factoriality was introduced by J. Coykendall and W. Smith in 2011 under the term "other-half-factoriality": they used length-factoriality to provide a characterization of unique factorization domains. In this paper, we study length-factoriality in the more general context of commutative, cancellative monoids. In addition, we study factorization properties related to length-factoriality, namely, the PLS property (recently introduced by Chapman et al.) and bi-length-factoriality in the context of semirings. [ABSTRACT FROM AUTHOR]

Let G be the two dimensional supersymmetric Galilean conformal algebra. In this paper, we obtain that Lie superalgebra G admits only triangular coboundary Lie super-bialgebra structures and the proof is mainly based on the computation of the first cohomology group of G with coefficients in the tensor product of its adjoint module. [ABSTRACT FROM AUTHOR]

Let k be an arbitrary field, Λ be a k-algebra and V be a Λ -module. When it exists, the universal deformation ring R (Λ , V) of V is a k-algebra whose local homomorphisms to R parametrize the lifts of V up to R ⊗ k Λ , where R is any complete, local commutative Noetherian k-algebra with residue field k. Symmetric special biserial algebras, which coincide with Brauer graph algebras, can be viewed as generalizing the blocks of finite type p-modular group algebras. Bleher and Wackwitz classified the universal deformation rings for all modules for symmetric special biserial algebras with finite representation type. In this paper, we begin to address the tame case. Specifically, let Λ be any 1-domestic, symmetric special biserial algebra. By viewing Λ as generalized Brauer tree algebras and making use of a derived equivalence, we classify the universal deformation rings for those Λ -modules V with stable endomorphism ring isomorphic to k. The latter is a natural condition, since it guarantees the existence of the universal deformation ring R (Λ , V) . [ABSTRACT FROM AUTHOR]

In the present paper, we investigate the universal PBW basis and HN system for the derived Hall algebra of a triangulated category satisfying some finiteness conditions. Furthermore, we study the related stability conditions on the module category A of the path algebra A of an acyclic quiver and on the bounded derived category of A. Moreover, we investigate the relation between the Ringel-Hall algebra and the HN system of A defined by Reineke. [ABSTRACT FROM AUTHOR]

In this paper, we define terms generated by transformations preserving a partition on a finite set and then construct their superassociative structures. A generating system of such algebra is determined and the freeness in a variety of all superassociative algebras is investigated. The connection between a semigroup of all mappings whose ranges are terms induced by transformations preserving a partition and substitutions is discussed. In views of applications, we apply these mappings to examine identities of a variety in a higher step. Additionally, we generalize our study to algebraic systems and establish a superassociative algebra of a new type of formulas induced by terms defined by transformations preserving a partition. [ABSTRACT FROM AUTHOR]

In this paper, for any prime p, we propose the notion of a p-transitive association scheme. This notion aims to generalize the fact that the regular module of a group algebra of a finite group has a unique principal submodule to the case of the regular modules of modular adjacency algebras of association schemes. We characterize the p-transitive quasi-thin association schemes and the p-transitive association schemes with thin thin residue by their structure theory properties. We also get some results with independent interests. [ABSTRACT FROM AUTHOR]

For a fixed integer n≥2, let Mn be the algebra of all n × n matrices over the complex field C. Let x1,x2∈Cn be two fixed nonzero vectors, and fix also y1,y2∈Cn. In this paper, we characterize linear bijective maps φ:Mn→Mn having the property that φ(A)φ(B)x2=y2 whenever ABx1=y1. [ABSTRACT FROM AUTHOR]

AbstractPre-Novikov algebras and quasi-Frobenius Novikov algebras naturally appear in the theory of Novikov bialgebras. In this paper, we show that there is a natural pre-Novikov algebra structure associated to a quasi-Frobenius Novikov algebra. Then we introduce the definition of double constructions of quasi-Frobenius Novikov algebras associated to two pre-Novikov algebras and show that it is characterized by a pre-Novikov bialgebra. We also introduce the notion of pre-Novikov Yang-Baxter equation, whose symmetric solutions can produce pre-Novikov bialgebras. Moreover, the operator forms of pre-Novikov Yang-Baxter equation are also investigated. [ABSTRACT FROM AUTHOR]

AbstractIn this paper we study certain combinatorial attributes of Ind-schemes of polynomial automorphisms in positive characteristic. In particular, we prove that over an algebraically closed field K of positive characteristic ≠2 every automorphism of the group of origin-preserving automorphisms of the polynomial algebra K[x1,…,xn] (n≥3), which fixes every diagonal matrix, preserves, up to composition with a linear inner automorphism, every tame automorphism. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

In this paper, we obtain a basis for the center of the infinitesimal q-Schur algebra s q (2 , r) 1 in terms of its certain basis. [ABSTRACT FROM AUTHOR]

AbstractFor a simple graph G with edge ideal I(G), we study the N -graded Betti numbers in the linear strand of the minimal free resolution of I(Γ(Zn)), where Γ(Zn) is the zero divisor graph of the ring Zn . We present sharp bounds for the Betti numbers of Γ(Zn) and characterize the graphs attaining these bounds, thereby establishing the correct equality case for one of the results of the earlier published paper (Theorem 4.5, S. Pirzada and S. Ahmad, On the linear strand of edge ideals of some zero divisor graphs, Commun. Algebra 51(2) (2023) 620–632). Also, we present homological invariants of the edge rings of Γ(Zn) for n=p2q and pqr, with primes p

AbstractIn this paper, all super-skewsymmetric super-biderivations of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are determined. It is shown that all the super-biderivations are inner. Furthermore, the linear super-commuting maps of twisted N = 1 Schrödinger-Neveu-Schwarz algebra are standard. [ABSTRACT FROM AUTHOR]

AbstractThe aim of this paper is to examine the structure of genetic algebras associated with permuted Lotka-Volterra operators on a finite-dimensional simplex. Furthermore, three dimensional permuted Lotka-Voltarra algebras are considered and the description of their derivations are given as well. [ABSTRACT FROM AUTHOR]

For a commutative ring R and a Hopf algebra H which is finitely generated projective as an R-module, it is established that there is an (anti)-isomorphism of groups between the Brauer group BQ(R, H) of Hopf Yetter-Drinfel'd H-module algebras and the Brauer group BQ (R , H *) of Hopf Yetter-Drinfel'd H * -module algebras, where H * is the linear dual of H. In this paper, we generalize this result by establishing an anti-isomorphism of groups between BQ(S, H), the Brauer group of dyslectic Hopf Yetter-Drinfel'd (S, H)-module algebras and BQ (S o p , H *) , the Brauer group of dyslectic Hopf Yetter-Drinfel'd (S o p , H *) -module algebras, where S is an H-commutative Hopf Yetter-Drinfel'd H-module algebra and Sop is the opposite algebra of S. Communicated by Alberto Elduque [ABSTRACT FROM AUTHOR]

The present paper is devoted to study local derivations on the conformal Galilei algebra. We prove that every local derivation on the conformal Galilei algebra is a derivation. [ABSTRACT FROM AUTHOR]

This paper aims to study the local derivations, 2-local automorphisms and local automorphisms on the super-Virasoro algebras. The primary focus is to establish that every local derivation of the super-Virasoro algebras is indeed a derivation, and to demonstrate that every local or 2-local automorphism of the super-Virasoro algebras is an automorphism. [ABSTRACT FROM AUTHOR]