Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
Papers published on a yearly basis
Papers
More filters
TL;DR: In this paper, the authors obtain Schur-Weyl dualities in which the algebras, acting on both sides, are semigroup algebras of various symmetric inverse semigroups and their deformations.
14 citations
TL;DR: In this article, it was shown that for a left (or right) P-restriction locally Ehresmann P-Ehresmann semigroup, if its projection set is principally finite, then the semigroup algebra of the semi-constant semigroup can be isomorphic to the category algebra of a corresponding category.
Abstract: P-Ehresmann semigroups are introduced by Jones as a common generalization of Ehresmann semigroups and regular $$*$$
-semigroups. Ehresmann semigroups and their semigroup algebras are investigated by many authors in literature. In particular, Stein shows that under some finiteness condition, the semigroup algebra of an Ehresmann semigroup with a left (or right) restriction condition is isomorphic to the category algebra of the corresponding Ehresmann category. In this paper, we generalize this result to P-Ehresmann semigroups. More precisely, we show that for a left (or right) P-restriction locally Ehresmann P-Ehresmann semigroup $$\mathbf{S}$$
, if its projection set is principally finite, then we can give an algebra isomorphism between the semigroup algebra of $$\mathbf{S}$$
and the partial semigroup algebra of the associate partial semigroup of $$\mathbf{S}$$
. Some interpretations and necessary examples are also provided to show why the above isomorphism dose not work for more general P-Ehresmann semigroups.
14 citations
TL;DR: In this paper, it was shown that if S is a finite aperiodic semigroup, then the semigroup generated by the functions {φs}s ∈ S is finite.
Abstract: Let S be a finite semigroup. In this paper, we introduce the functions φs:S* → S*, first defined by Rhodes, given by φs([a1,a2,…,an]) = [sa1,sa1a2,…,sa1a2 ⋯ an]. We show that if S is a finite aperiodic semigroup, then the semigroup generated by the functions {φs}s ∈ S is finite and aperiodic.
14 citations
TL;DR: In this article, the commutativity of addition and multiplication of near-rings satisfying certain identities involving n-derivations on semigroup ideals and ideals is investigated, and conditions with semigroup ideal for n -derivation D 1 and D 2 of N are studied.
14 citations
01 Jan 1984
TL;DR: In this paper, it was shown that a product may be defined in M(βS) without reference to l1(S), the space of continuous functions on the Stone-Cech compactification of S. This was shown to be possible even when S is a non-discrete semitopological semigroup, provided that the operation in S may be extended to make βS into a left-topological semiigroup.
Abstract: If S is an infinite, discrete, commutative semigroup then the semigroup algebra l1(S) is a commutative Banach algebra. Its dual is l∞(S), which is isometrically iso-morphic to C(βS), the space of continuous functions on the Stone-Cech compactification of S. This fact enables us to identify the second dual of l1(S) with M(βS), the space of bounded regular Borel measures on βS. Endowed with the Arens product the second dual is also a Banach algebra, so it is natural to ask whether a product may be defined in M(βS) without reference to l1(S). In §4 this is shown to be possible even when S is a non-discrete semitopological semigroup, provided that the operation in S may be extended to make βS into a left-topological semigroup in the manner of, for example, [2] where further references may be found. (Note, however, that the construction there is of a right-topological semigroup.) Having done this we may use results on βS to provide information about the measure algebra.
14 citations