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 notions of causal paths and causal homotopies were introduced for certain basic constructions in (Lie) semigroup theory, and the major result is the construction in this causal context of an analogue of the universal covering semigroup and the demonstration that local homomorphisms on the given semigroup extend to global homomorphism on it.
Abstract: We introduce the notions of causal paths and causal homotopies, modifications of the traditional notions of paths and homotopies, as more suitable for certain basic constructions in (Lie) semigroup theory. The major result is the construction in this causal context of an analogue of the universal covering semigroup and the demonstration that local homomorphisms on the given semigroup extend to global homomorphisms on it. In certain important cases, it is shown that this semigroup actually agrees with the universal covering semigroup.
9 citations
TL;DR: In this article, the structure of semigroups that satisfy the following properties of generalised inflation of a band is determined: the direct product of a group and a band, a completely simple semigroup and a free semigroup F(X).
Abstract: We determine the structure of semigroups that satisfy xyzw∈{xy,xw,zy,zw}. These semigroups are precisely those whose power semigroup is a generalised inflation of a band. The structure of generalised inflations of the following types of semigroups is determined: the direct product of a group and a band, a completely simple semigroup and a free semigroup F(X) on a set X. In the latter case the semigroup must be an inflation of F(X). We also prove that in any semigroup that equals its square, the power semigroup is a generalised inflation of a band if and only if it is an inflation of a band.
9 citations
9 citations
TL;DR: In this article, the structure of left cancellative semigroups is described, and the existence of idempotents is investigated, and it is shown that the existence is related to maximal proper right ideals.
Abstract: In this note we shall describe the structure of left cancellative semigroups. We shall also investigate the existence of idempotents and show that the existence of idempotents is related to the existence of maximal proper right ideals.
9 citations
TL;DR: It is proved that a finitely presented Rees quotient of a free inverse semigroup has polynomial or exponential growth, and that the type of growth is algorithmically recognizable.
Abstract: We prove that a finitely presented Rees quotient of a free inverse semigroup has polynomial or exponential growth, and that the type of growth is algorithmically recognizable. We prove that such a semigroup has polynomial growth if and only if it satisfies a certain semigroup identity. However we give an example of such a semigroup which has exponential growth and satisfies some nontrivial identity in signature with involution.
9 citations