Isomorphisms via Congruences on \Gamma -Semigroups and \Gamma -Ideals

H. Hedayati

Abstract

The notion of $\Gamma$-semigroup introduced in \cite{24} as a generalization of a semigroup. In this paper, we investigate the formation of quotient and generated $\Gamma$-semigroups and $\Gamma$-ideals. Also, by a congruence relation $\rho$ on a $\Gamma$-semigroup $S$, we construct the quotient $\Gamma$-semigroup $S:\rho$ and discuss on the behavior of some diagrams of quotients and their commutativity. In particular, we prove that the product of quotient $\Gamma$-semigroups is isomorphic to the quotient of product of $\Gamma$-semigroups.