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, it was shown that if B is the bicyclic semigroup, then a certain inverse subsemigroup F of B × B is a free elementary inverse semigroup.
Abstract: The purpose of this note is to give a characterization of a free inverse semigroup on a singleton set. It will be shown that if B is the bicyclic semigroup, then a certain inverse subsemigroup F of B × B is a free elementary inverse semigroup.
19 citations
TL;DR: In this paper, a solution to the Diophantine Frobenius problem for pseudo-symmetric numerical semigroups with embedding dimension three is given, and a presentation for this kind of semigroup and a formula to determine whether or not such a numerical semigroup is pseudo symmetric is given.
19 citations
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TL;DR: In this paper, the full and reduced C*-algebras of the left inverse hull of a semigroup were shown to be isomorphic, and conditions ensuring that these are isomorphic.
Abstract: To each discrete left cancellative semigroup $S$ one may associate a certain inverse semigroup $I_l(S)$, often called the left inverse hull of $S$. We show how the full and the reduced C*-algebras of $I_l(S)$ are related to the full and reduced semigroup C*-algebras for $S$ recently introduced by Xin Li, and give conditions ensuring that these algebras are isomorphic. Our picture provides an enhanced understanding of Li's algebras.
19 citations
TL;DR: In this article, the authors introduced a polynomial time algorithm for the local testability problem and to find the level of locally testability for semigroups based on their previous description of identities of k-testable semiigroups and the structure of locally tested semigroup.
Abstract: A locally testable semigroup S is a semigroup with the property that for some non-negative integer k, called the order or level of local testability, two words u and v in some set of generators for S are equal in the semigroup if (1) the prefix and suffix of the words of length k coincide, and (2) the set of intermediate substrings of length k of the words coincide. The local testability problem for semigroups is, given a finite semigroup, to decide, if the semigroup is locally testable or not. Recently, we introduced a polynomial time algorithm for the local testability problem and to find the level of local testability for semigroups based on our previous description of identities of k-testable semigroups and the structure of locally testable semigroups. The first part of the algorithm we introduce solves the local testability problem. The second part of the algorithm finds the order of local testability of a semigroup. The algorithm is of order n2, where n is the order of the semigroup.
19 citations
19 citations