Motivated by studying various classes of bisimple inverse semigroups with special semilattices of idempotents, and as a continuation of Reilly description of bisimple inverse ω − semigroups. In this paper, we introduce the concept of generalized Bruck–Reilly extensions. We call a (right) type B ω − semigroup with the generalized Bruck–Reilly extension a ∼ bisimple (right) type B ω − semigroup. After obtaining some basic properties and characterizations of this class of semigroups, we get sufficient and necessary conditions for an arbitrary ∼ bisimple (right) type B ω − semigroup to be a (right) type B semigroup. Finally, we get structure theorems for some special cases of such semigroups and give an application of our results.

On ∼ bisimple right type B ω− semigroups as model of some fractal structure

Abstract The aim of this paper is to study the translational hull of a strongly right type B semigroup. Our main result is to prove that the translational hull of a strongly right type B semigroup is itself a strongly right type B semigroup. As an application, we give a proof of a problem posted by Petrich on translational hulls of inverse semigroups in Petrich (Inverse Semigroups, Wiley, New York, 1984) to the cases of some strongly right type B semigroups.

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A characterization of translational hulls of a strongly right type B semigroup

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A new characterization of a proper type B semigroup

In this paper, we will investigate the natural partial orders on IC-abundant semigroups. After giving some properties and characterizations of natural partial orders on abundant semigroups, we consider IC-abundant semigroups. We prove that an IC-abundant semigroup is locally ample if and only if the natural partial order on the semigroup is compatible with the multiplication.

On Natural Partial Orders of IC-Abundant Semigroups

The concept of a proper cover of a right type B semigroup is introduced.Furthermore,it is proved that any proper cover for a right type B semigroup is a proper cover over a left cancellative monoid.A structure theorem of proper covers for a right type B semigroup is also given.

Wang Limin

Papers

A Proper Cover on a Right Type B Semigroup