Strictly Orthodox Bisimple Semigroups of Type-ω, I

Abstract

The purpose of this paper is to describe the structure of strictly orthodox bisimple semigroups of type-ω.

Since E(S) E(T), E(S) is a sub semigroup of S. Hence S is an orthodox semigroup in the sense of Hall (3). Now, if Green's relations Rand L are congruence relations on both T and E(S) then we call S a strictly orthodox bisimple semigroup of type-ω.