A Class of ∗-Simple Type $A$ $ω^2$ -Semigroups (I)

Abstract

In this paper, we study ∗-simple type $A$ $ω^2$-semigroups in which $\mathcal{D}^∗ = \widetilde{D}$ and $\mathcal{D}^∗|_{E_S} = \mathcal{M}_d$ by the generalized Bruck-Reilly extension and obtain its structure theorem. We also obtain a criterion for isomorphisms of two such semigroups.