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In this paper, we prove the generalized Hyers-Ulam stability of homomorphisms in quasi-Banach algebras associated with the following Pexiderized Jensen functional equation This is applied to investigating homomorphisms between quasi-Banach algebras. The concept of the generalized Hyers-Ulam stability originated from Rassias’ stability theorem that appeared in his paper: On the stability of the linear mapping in Banach spaces, Proc. Amer. Math. Soc., 72, 297–300 (1978). [ABSTRACT FROM AUTHOR]

The present paper continues a series of papers of the author (some of them are written in collaboration), in which the Yoneda algebras are calculated for several families of algebras of dihedral and semidihedral type (in K. Erdmann’s classification). In the paper, the Yoneda algebras are described (in terms of quivers with relations) for the algebras of semidihedral type that form the family SD(3 $$\mathcal{K}$$ ). Bibliography: 10 titles. [ABSTRACT FROM AUTHOR]

For homotopies of quasigroups, an analog of the fundamental theorem on homomorphisms does not hold in general. In this paper, we consider two approaches that allow one to obtain an analog of this theorem: the introduction of strict homotopies and the move from quasigroups to three-sorted quasigroups. [ABSTRACT FROM AUTHOR]

The aim of the present paper is to explicitly construct canonical representatives in every strict isomorphism class of commutative formal groups over an arbitrary torsion-free ring. The case of an Z( p) -algebra is treated separately. We prove that, under natural conditions on a subring, the canonical representatives of formal groups over the subring agree with the representatives for the ring. Necessary and sufficient conditions for a mapping induced on strict isomorphism classes of formal groups by a homomorphism of torsion-free rings to be injective and surjective are established. [ABSTRACT FROM AUTHOR]

We introduce an efficient algorithm to compute the homomorphism induced in (relative) homology by a continous map. The algorithm is based on a cubical approximation of the map and the theory of multivalued maps. A software implementation of the algorithms introduced in this paper is available at [27]. [ABSTRACT FROM AUTHOR]

The results of Kasparov, Connes, Higson, and Loring imply the coincidence of the functors [[ qℂ ⊗ K, B ⊗ K]] = [[ C0(ℝ2) ⊗ K, B ⊗ K]] for any C*-algebra B; here[[ A, B]] denotes the set of homotopy classes of asymptotic homomorphisms from A to B. Inthe paper, this assertion is strengthened; namely, it is shown that the algebras qℂ ⊗ K and C0(ℝ2) ⊗ K are equivalent in the category whose objects are C*-algebras and morphisms are classes of homotopic asymptotic homomorphisms. Some geometric properties of the obtained equivalence are studied. Namely, the algebras qℂ ⊗ K and C0(ℝ2) ⊗ K are represented as fields of C*-algebras; it is proved that the equivalence is not fiber-preserving, i.e., is does not take fibers to fibers. It is also proved that the algebras under consideration are not homotopy equivalent. [ABSTRACT FROM AUTHOR]

In this paper we study the structure of positive homomorphisms on real function algebras. We prove that every positive homomorphism is completely characterized by a family of sets and when the algebra is invert-closed, by an ultrafilter of zero-sets of functions of the algebra. We show that the known sufficient conditions for every homomorphism of a real function algebra to be countably evaluating or a point evaluation are not necessary. Our results enable us to characterize the countably evaluating algebras as well as the Lindelöf spaces as the spaces in which for every algebra, each countably evaluating homomorphism is a point evaluation. [ABSTRACT FROM AUTHOR]

Pseudoeffect (PE) algebras have been introduced as a noncommutative generalization of effect algebras. We study in this paper PE algebras with the special property of having a nonempty state space. To this end, we consider PE algebras which are po-group intervals and which are, in a certain sense, noncommutative only in the small. Such a PE algebra is shown to possess a nontrivial commutative homomorphic image from which then follows that there exist states. A typical example is given by an interval of the lexicographical product of two po-groups the first of which is abelian. [ABSTRACT FROM AUTHOR]