Showing papers on "Bicyclic semigroup published in 2018"
TL;DR: In this article, necessary and sufficient conditions for a semigroup identity to hold in the monoid of n × n upper triangular matrices, in terms of equivalence of certain tropical polynomials, were established.
33 citations
TL;DR: In this article, the authors introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group and describe it as a semigroup C*-algebra.
Abstract: We introduce algebraic dynamical systems, which consist of an action of a right LCM semigroup by injective endomorphisms of a group. To each algebraic dynamical system we associate a C*-algebra and describe it as a semigroup C*-algebra. As part of our analysis of these C*-algebras we prove results for right LCM semigroups. More precisely we discuss functoriality of the full semigroup C*-algebra and compute its K-theory for a large class of semigroups. We introduce the notion of a Nica-Toeplitz algebra of a product system over a right LCM semigroup, and show that it provides a useful alternative to study algebraic dynamical systems.
33 citations
TL;DR: A variant of Schreier's Theorem, and the theory of Green's relations, are shown how to reduce the computation of an arbitrary subsemigroup of a finite regular semigroup to that of certain associated subgroups.
25 citations
TL;DR: In this paper, the authors provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space.
Abstract: In this manuscript we provide a review on the classical and resent results related to the problem of analytic extension in parameter for a semigroup of holomorphic self-mappings of the unit ball in a complex Banach space and its relation to the linear continuous semigroup of composition operators.
9 citations
TL;DR: In this article, a set of orthogonal idempotents is constructed for an ℛ-unipotent semigroup such that the set E(S) is locally ℒ-finite and R is a commutative ring with identity.
Abstract: Let S be an ℛ-unipotent semigroup such that the idempotent set E(S) is locally ℒ-finite, and let R be a commutative ring with identity. In this paper, we construct a set of orthogonal idempotents {...
4 citations
TL;DR: In this paper, the authors characterized pseudo-amenability of semigroup algebras for a certain class of commutative semigroups S, the so-called archimedean semigroup.
Abstract: In this paper, we first characterize pseudo-amenability of semigroup algebras $$\ell ^1(S),$$
for a certain class of commutative semigroups S, the so-called archimedean semigroups. We show that for an archimedean semigroup S, pseudo-amenability, amenability and approximate amenability of $$\ell ^1(S)$$
are equivalent. Then for a commutative semigroup S, we show that pseudo-amenability of $$\ell ^{1}(S)$$
implies that S is a Clifford semigroup. Finally, we give some results on pseudo-amenability and approximate amenability of the second dual of a certain class of commutative semigroup algebras $$\ell ^1(S)$$
.
3 citations
TL;DR: In this article, a ℤ-graded structure of the Toeplitz algebra was constructed and the types of these algebras with respect to the ToEplitz algebra were determined.
Abstract: We construct a ℤ-graded structure of the Toeplitz algebra and consider nuclear C
*
-subalgebras of the Toeplitz algebra generated by inverse subsemigroups of a bicyclic semigroup. The types of these algebras with respect to the Toeplitz algebra are determined. In addition, it is shown that the considered algebras are equipped with the structure of Hilbert C
*
-modules.
2 citations
TL;DR: In this paper, it was shown that the class of all idempotent semigroups is globally determined if any two members of a semigroup with isomorphic globals are themselves isomorphic.
Abstract: The power semigroup, or global, of a semigroup S is the set 𝒫(S) of all nonempty subsets of S equipped with the naturally defined multiplication. A class 𝒦 of semigroups is globally determined if any two members of 𝒦 with isomorphic globals are themselves isomorphic. The principal goal of this paper is to prove that the class of all idempotent semigroups is globally determined.
1 citations
TL;DR: The super B-quasi-Ehresmann semigroup as discussed by the authors is an analogy of an orthodox semigroup within the class of B-semiabundant semigroups.
Abstract: We first study the structure of a special generalized regular semigroup, namely the B-semiabundant semigroup which can be expressed as the join of the pseudo-varieties of finite groups and finite aperiodic groups. In the literature, the weakly B-semiabundant semigroups have recently been thoughtfully investigated and considered by Wang. One easily observes that the class of good B-semiabundant semigroups is a special class of semigroups embraces all abundant (and hence regular) semigroups. In particular, a super B-quasi-Ehresmann semigroup is an analogy of an orthodox semigroup within the class of B-semiabundant semigroups. Thus, the class of super B-quasi-Ehresmann semigroups is obviously a subclass of the class of good B-quasi-Ehresmann semigroups which contains all orthodox semigroups. Thus, the super B-quasi-Ehresmann semigroup behaves similarly as the Clifford subsemigroups within the class of regular semigroups. Consequently, a super B-quasi-Ehresmann semigroup is now recognized as an important generalized regular semigroup. Our aim in this paper is to describe the properties and intrinsic structure of a super B-quasi-Ehresmann semigroup whose band of projections is right regular, right normal, left semiregular, left seminormal, regular, left quasinormal or normal, respectively. Hence, our representation theorem of the super B-quasi-Ehresmann semigroups improves, strengthens and generalizes the well-known “standard representation theorem of an orthodox semigroup” established by He et al. (Commun. Algebra 33:745–761, 2005). Finally, a general representation theorem in the category of Ehresmann semigroups is given.
TL;DR: In this paper, the relation among generalized path algebras, pseudo-admissible ordered semi-geneges, and path alges over algesbras is investigated.
Abstract: The aim of this paper is to research the relation among generalized path algebras, pseudo-admissible ordered semigroup algebras and path algebras over algebras. First, the Gabriel theorem f...