ArticleOriginal scientific text
Title
Wreath product of a semigroup and a Γ-semigroup
Authors 1, 2
Affiliations
- Department of Pure Mathematics, University of Calcutta 35, Ballygunge Circular Road, Kolkata-700019, India
- Sri Ramkrishna Sarada Vidyamahapitha Kamarpukur, Hooghly-712612, West Bengal, India
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 Γ-semigroup and investigate some interesting properties of this product.
Keywords
semigroup, Γ-semigroup, orthodox semigroup, right(left) orthodox Γ-semigroup, right(left) inverse semigroup, right(left) inverse Γ-semigroup, right(left)α-unity, Γ-group, semidirect product, wreath product
Bibliography
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Pages:
161-178
Main language of publication
English
Received
2007-08-10
Accepted
2007-09-14
Published
2008
DOI: 10.7151/dmgaa.1141
Exact and natural sciences