Author
G. B. Preston
Bio: G. B. Preston is an academic researcher from Monash University, Clayton campus. The author has an hindex of 1, co-authored 1 publications receiving 21 citations.
Papers
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TL;DR: In this paper, alternative characterizations of semidirect products of semigroups are given, such as groups, regular semiggroups, and inverse semiigroups. But they do not consider the relation between groups and regular semigenes.
Abstract: Two alternative characterizations of semidirect products of semigroups are given. Characterizations are provided of such products that are groups, regular semigroups, and inverse semigroups, respectively.
22 citations
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TL;DR: In this paper, some special congruences on E-inversive E-semigroups are investigated, such as the least group congruence, a certain semilattice con-gruence and a certain idempotent-separating concongruence.
Abstract: A semigroup S is called E-inversive if for every a ∈ S there exists x ∈ S such that ax is idempotent. S is called E-semigroup if the set of idempotents of S forms a subsemigroup. In this paper some special congruences on E-inversive E-semigroups are investigated, such as the least group congruence, a certain semilattice congruence, some regular congruences and a certain idempotent-separating congruence.
28 citations
TL;DR: In this paper, the authors provide set-theoretical solutions of the Yang-Baxter equation that are not necessarily bijective, among these new idempotent ones.
16 citations
Abstract: A semigroup S is called E-inversive if for every a ∈ S there is an x ∈ S such that ax is idempotent. The purpose of this paper is the investigation of E-inversive semigroups and semigroups whose idempotents form a subsemigroup. Basic properties are analysed and, in particular, semigroups whose idempotents form a semilattice or a rectangular band are considered. To provide examples and characterizations, the construction methods of generalized Rees matrix semigroups and semidirect products are employed.
9 citations
TL;DR: In this paper, the concept of left wreath products of semigroups was introduced, and it was shown that the ℒ*-inverse semigroup can be described as the left wreaths product of a type A semigroup and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B).
Abstract: The concepts of ℒ*-inverse semigroups and left wreath products of semigroups are introduced. It is shown that the ℒ*-inverse semigroup can be described as the left wreath product of a type A semigroup Γ and a left regular band B together with a mapping which maps the semigroup Γ into the endomorphism semigroup End(B). This result generalizes the structure theorem of Yamada for the left inverse semigroups in the class of regular semigroups. We shall also provide a constructed example for the ℒ*-inverse semigroups by using the left wreath products.
9 citations
TL;DR: In this article, a construction theorem of Q ⁎ -inverse semigroups is given by using the wreath product of some semigroup, and it is proved that a semigroup S is a Q � -INverse semigroup if and only if it is a spined product of an L ⎉ -inversely semigroup and an R ⁉-inverse semiigroup.
8 citations