On q *-bisimple IC semigroups of type-E

Abstract

A semigroup is called type-E if the band of its idempotents can be expressed as a direct product of a rectangular band and an ω-chain. For brevity, we call an IC *-bisimple quasi-adequate semigroup of type-E a q*-bisimple IC semigroup of type-E. In this paper, we characterize q*-bisimple semigroups by using some kind of generalized Bruck-Reilly extensions. As a consequence, some results concerning *-bisimple type-Aω-semigroups given by Asibong-Ibe (Semigroup Forum 31:99–117, 1985) are generalized.