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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24 Feb 2005
TL;DR: In this article, a group G such that G contains a free noncyclic subgroup (hence, G satisfies no group identity) and G, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity is constructed.
Abstract: To solve two problems of Bergman stated in 1981, we construct a group G such that G contains a free noncyclic subgroup (hence, G satisfies no group identity) and G, as a group, is generated by its subsemigroup that satisfies a nontrivial semigroup identity.
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 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
TL;DR: In this article, the Baer-Levi semigroup on X is defined as the set of all injective total transformations α: X → X such that | X \ X α| = q.
Abstract: Let X be an infinite set and suppose א 0 ≤ q ≤ | X |. The Baer-Levi semigroup on X is the set of all injective ‘total’ transformations α: X → X such that | X \ X α| = q . It is known to be a right simple, right cancellative semigroup without idempotents, its automorphisms are “inner”, and some of its congruences are restrictions of Malcev congruences on I ( X ), the symmetric inverse semigroup on X . Here we consider algebraic properties of the semigroup consisting of all injective ‘partial’ transformations α of X such that | X \ X α| = q : in particular, we descried the ideals and Green's relations of it and some of its subsemigroups.
5 citations