Topic
Cancellative semigroup
About: Cancellative semigroup is a research topic. Over the lifetime, 1320 publications have been published within this topic receiving 13319 citations.
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TL;DR: In this paper, the authors describe the structure of WA in the singular case and the criterion for distributivity of the M -modules WCd' since the necessary conditions for that established in [ 1: 8.51 limit d tod
25 citations
TL;DR: In this paper, an example of such an involution semigroup of order n + 5 for any positive integer n is presented, and the reduct of which is non-nitely based.
Abstract: Since the study of the nite basis problem for nite semigroups began in the 1960s, it has been unknown if there exists any nite involution semigroup that is nitely based but the reduct of which is non-nitely based. The present article exhibits an example of such an involution semigroup of order n + 5 for any positive integer n.
25 citations
25 citations
TL;DR: In this article, the pseudo-amenability of semigroup algebra l1(S) is investigated, where S is an inverse semigroup with uniformly locally finite idempotent set.
Abstract: In this paper, we investigate the pseudo-amenability of semigroup algebra l1(S), where S is an inverse semigroup with uniformly locally finite idempotent set. In particular, we show that for a Brandt semigroup \(S={\mathcal{M}}^{0}(G,I)\), the pseudo-amenability of l1(S) is equivalent to the amenability of G.
25 citations
TL;DR: In this paper, the authors studied the semigroup of partial co-final monotone bijective transformations of the set of positive integers and showed that it has algebraic properties similar to the bicyclic semigroup.
Abstract: In this paper we study the semigroup $\mathscr{I}_{\infty}^{
earrow}(\mathbb{N})$ of partial cofinal monotone bijective transformations of the set of positive integers $\mathbb{N}$. We show that the semigroup $\mathscr{I}_{\infty}^{
earrow}(\mathbb{N})$ has algebraic properties similar to the bicyclic semigroup: it is bisimple and all of its non-trivial group homomorphisms are either isomorphisms or group homomorphisms. We also prove that every locally compact topology $\tau$ on $\mathscr{I}_{\infty}^{
earrow}(\mathbb{N})$ such that $(\mathscr{I}_{\infty}^{
earrow}(\mathbb{N}),\tau)$ is a topological inverse semigroup, is discrete. Finally, we describe the closure of $(\mathscr{I}_{\infty}^{
earrow}(\mathbb{N}),\tau)$ in a topological semigroup.
24 citations