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 article, the structure of inverse semigroup extensions by any other is analyzed in the case where R is a semilattice and a brief preliminary examination is made of a certain class of congruences, on inverse semigroups, which are intimately related to such extensions.
Abstract: The structure of inverse semigroup extensions of one inverse semigroup R by any other is analyzed in the case where R is a semilattice. Both a representation and method of construction are given. A brief preliminary examination is made of a certain class of congruences, on inverse semigroups, which are intimately related to such extensions.
13 citations
13 citations
TL;DR: In this article, the subsemigroup T(X,Y) of the full transformation semigroup on a set X and a nonempty Y⊆X is shown to be right abundant but not left abundant whenever Y is a proper non-singleton subset of X.
Abstract: Given a set X and a nonempty Y⊆X, we denote by T(X,Y) the subsemigroup of the full transformation semigroup on X consisting of all transformations whose range is contained in Y. We show that the semigroup T(X,Y) is right abundant but not left abundant whenever Y is a proper non-singleton subset of X.
13 citations
TL;DR: This work has implemented the Delorme algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and telescopic numerical Semigroups, and numerical semIGroups associated to an irreducible plane curve singularity.
Abstract: Delorme suggested that the set of all complete intersection numerical semigroups can be computed recursively. We have implemented this algorithm, and particularized it to several subfamilies of this class of numerical semigroups: free and telescopic numerical semigroups, and numerical semigroups associated to an irreducible plane curve singularity. The recursive nature of this procedure allows us to give bounds for the embedding dimension and for the minimal generators of a semigroup in any of these families.
13 citations
TL;DR: The non-commutative version of this theorem is unsettled as discussed by the authors, and it is not known whether a group with zero is a R-semigroup unless it admits a ring structure.
Abstract: A multiplicative semigroup S with 0 is said to be a R-semigroup if S admits a ring structure. Isbell proved that if a finitely generated commutative semigroup is a R-semigroup, then it should be finite. The non-commutative version of this theorem is unsettled. This paper considers semigroups, not necessarily commutative, which are principally generated as a right ideal by single elements and semigroups which are generated by two independent generators and describes their structure. We also prove that if a cancellative 0-simple semigroup containing an identity is a R-semigroup, then it should be a group with zero.
13 citations