Journal ArticleDOI
Wreath product of a semigroup and a Γ-semigroup
M. K. Sen,Sumanta Chattopadhyay +1 more
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In this article, the semidirect product of a semigroup and a Γ-semigroup is studied and some interesting properties of this product are investigated. And the notion of wreath product is introduced.Abstract:
Let S = {a, b, c, . . .} and Γ = {α, β, γ, . . . } be two nonempty sets. S is called a Γ-semigroup if aαb ∈ S, for all α ∈ Γ and a, b ∈ S and (aαb)βc = aα(bβc), for all a, b, c ∈ S and for all α, β ∈ Γ. In this paper we study the semidirect product of a semigroup and a Γ-semigroup. We also introduce the notion of wreath product of a semigroup and a Γsemigroup and investigate some interesting properties of this product.read more
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Book ChapterDOI
\(\Gamma \)-Semigroups: A Survey
M. K. Sen,S. Chattopadhyay +1 more
TL;DR: A survey of some works published by different authors on the concept of gamma-semigroups can be found in this article, where the authors present a survey of the generalization of semigroups.
Journal ArticleDOI
E-Inversive Γ-Semigroups
M. K. Sen,Sumanta Chattopadhyay +1 more
TL;DR: In this article, the authors investigate different properties of E-inversive -semigroup and right E-semigroup, and show that a right E--semigroup is a -idempotent.
References
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Journal ArticleDOI
Right (left) inverse semigroups
TL;DR: A semigroup S (with zero) is called a right inverse semigroup if every (nonnull) principal left ideal of S has a unique idempotent generator as discussed by the authors.
Journal ArticleDOI
On the regularity of semidirect products
TL;DR: In this article, necessary and sufficient conditions for the semidirect product of two monoids to be regular were determined for the case where the monoid product is a regular monoid.