International Journal of Mathematics and Mathematical Sciences
Volume 13 (1990), Issue 3, Pages 527-534
doi: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 M. K. Sen and N. K. Saha. 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 aαb∈M, for α∈Γ and b∈M and (aαb)βc=aα(bβc), for all a,b,c∈M and for all α,β∈Γ. 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.