Topic
Bicyclic semigroup
About: Bicyclic semigroup is a research topic. Over the lifetime, 1507 publications have been published within this topic receiving 19311 citations.
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5 citations
TL;DR: In this article, the authors investigated some further properties of one-dimensional tiling semigroups as a particular case of the inverse semigroup associated with a factorial language and obtained a presentation for the semigroup and its description as a P*-semigroup.
Abstract: In this article, we investigate some further properties of one-dimensional tiling semigroups as a particular case of the inverse semigroup associated with a factorial language. Namely, a presentation for the semigroup and its description as a P*-semigroup are obtained. Since both cons-truc-tions rely on the language, these properties highlight the deep connection between the semigroup and the language associated with a one-dimensional tiling semigroup.
5 citations
TL;DR: In this paper, it was shown that the initial linear relation is a generator of a semigroup of operators, and that the original linear relation can be seen as a function of the generator of the semigroup.
Abstract: Given a linear relation (multivalued linear operator) with certain growth restrictions on the resolvent, an infinitely differentiable semigroup of operators is constructed. It is shown that the initial linear relation is a generator of this semigroup. The results obtained are intimately related to certain results in the monograph “Functional analysis and semi-groups” by Hille and Phillips. §
5 citations
TL;DR: In this article, a class of inverse semigroups of injective transformations is introduced, and the main result concerns isomorphisms between two such semigroup, and it is shown that the two inverse semiigroups under consideration are isomorphic if and only if the corresponding topological spaces are homeomorphic.
Abstract: We introduce a class of inverse semigroups of injective transformations and our main result concerns isomorphisms between two such semigroups. This result is then applied to semigroups of homeomorphisms between closed subsets of a T 1 topological space, semigroups of homeomorphisms between compact subsets of k -spaces and semigroups of isomorphisms between subsemilattices of semilattices. In the first two cases it is shown that the two inverse semigroups under consideration are isomorphic if and only if the corresponding topological spaces are homeomorphic. In the latter case, the two inverse semigroups are isomorphic if and only if the semilattices are either isomorphic or are dual isomorphic infinite chains.
5 citations
TL;DR: In this paper, the authors investigated the question of when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses.
Abstract: We investigate the question as to when the members of a finite regular semigroup may be permuted in such a way that each member is mapped to one of its inverses. In general this is not possible. However we reformulate the problem in terms of a related graph and, using an application of Hall’s Marriage Lemma, we show in particular that the finite full transformation semigroup does enjoy this property.
5 citations