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Right C-restriction semigroups are the common generalizations of right C-rpp semigroups and right C-lpp semigroups. The structure of such a semigroup is established in terms of the Δ -product of a right regular band and a C-restriction semigroup. As its applications, we give the structures of right C-rpp semigroups and right C-lpp semigroups. Also, we give the dual wreath product structure of right C-restriction semigroups. These results extend the related results in (Semigroup Forum 68 (2004) 280–292) and (Algebra Colloquium 14 (2007) 285–294). [ABSTRACT FROM AUTHOR]

The notions of regular, intra regular and duo bi-acts of a Morita context of monoids have been introduced. Some characterizations of regular and intra regular bi-acts have been obtained in terms of b-subacts. Also connections among regularity of acts and k -regularity of power semimodules, intra regularity of acts and intra k -regularity of power semimodules have been observed using power functor. Then the study of the interplay among various components of a Morita context of monoids in terms of regularity, intra regularity and duoness have been accomplished. It has been deduced that regularity, intra regularity and being duo are Morita invariant properties. Finally regular (intra regular, duo) Morita context has been defined and it has been proved that for a duo Morita context of monoids regular and intra regular Morita context coincide. [ABSTRACT FROM AUTHOR]

In this paper, the notion of closed cubic intuitionistic ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals in BCI-algebras are introduced, and several related properties are investigated. Relations between cubic intuitionistic subalgebras, closed cubic intuitionistic ideals, cubic intuitionistic q-ideals, cubic intuitionistic p-ideals and cubic intuitionistic a-ideals are discussed. Conditions for a cubic intuitionistic ideal to be a cubic intuitionistic p-ideal are provided. Characterizations of a cubic intuitionistic a-ideal are considered. The cubic intuitionistic extension property for a cubic intuitionistic a-ideal is established.

In this paper, our aim is to introduce the notion of a composition (m, n, k)-hyperring and to analyze its properties. We also consider the algebraic structure of (m, n, k) hyperrings which is a generalization of composition rings and composition hyperrings. Also, the isomorphism theorems of ring theory are derived in the context of composition (m, n, k)-hyperrings.

In this work, h w -lifting modules, a special extension of h -lifting which is a further generalization of lifting modules, are studied. Here, we observed that finite direct sum of h w -lifting modules may not be h w -lifting, so we provided various sufficient conditions for which h w -lifting modules are closed under direct sum. Moreover, we have introduced and studied the properties of a new version of h -lifting module namely, m h -lifting, m h w -lifting and completely m h -lifting modules and develop some more properties of the h w -lifting modules in terms of these modules. Further, we proved that if the direct sum of arbitrary family of hollow modules is m h -lifting, then the arbitrary direct sum of m h -lifting R -module is again m h -lifting. [ABSTRACT FROM AUTHOR]

The hypothesis of an ordered b-semiring provides a characterization of semiring and ordered semiring in this paper. We have attempted to investigate the Type-1 bi-ideal, Type-2 bi-ideal, Type-1 bi-base and Type-2 bi-base over ordered b-semiring in detail. Some of their characterizations are obtained through Type-1 bi-base and Type-2 bi-base. Let ℋ be a Type-1 (Type-2) bi-base of ordered b-semiring and a , b ∈ ℋ such that a ≠ b but not a ≤ t 1 b b , nor b ≤ t 1 b a (a ≤ t 2 b b , nor b ≤ t 2 b a). We introduce the notions of one-quasi order and two-quasi order on an ordered b -semiring to interact with Type-1 and Type-2 bi-bases generated by element and subset. With the help of some examples, we have shown that Type-1 bi-base and Type-2 bi-base have partial order. [ABSTRACT FROM AUTHOR]

The investigation of orthodox P -restriction semigroups was initiated by Jones in 2014 as generalizations of orthodox * -semigroups. The aim of this paper is to further study orthodox P -restriction semigroups based on the known results of Jones. After establishing a construction theorem for orthodox P -restriction semigroups, we introduce proper P -restriction semigroups (which are necessarily orthodox) and prove that every (finite) orthodox P -restriction semigroup has a (finite) proper cover. Our results enrich and extend existing results for restriction semigroups and orthodox * -semigroups. [ABSTRACT FROM AUTHOR]