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International Journal of Mathematics and Mathematical Sciences
Volume 13, Issue 3, Pages 527-534
http://dx.doi.org/10.1155/S016117129000076X

Orthodox Γ-semigroups

1Department of Pure Mathematics, 35, Ballygunge Circular Road, Calcutta 700 019, India
2Department of Mathematics, Pingla Thana Mahavidyalaya, P.O. Maligram, Dist. Midnapore, Pin, 721 140, India

Received 7 December 1988

Copyright © 1990 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

Let M={a,b,c,} and Γ={α,β,γ,} be two non-empty sets. M is called a Γ-semigroup if aαbM, for αΓ and bM and (aαb)βc=aα(bβc), for all a,b,cM and for all α,βΓ. A semigroup can be considered as a Γ-semigroup. In this paper we introduce orthodox Γ-semigroups and extend different results of orthodox semigroups to orthodox Γ-semigroups.