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

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−ω− semigroups. In this paper, we introduce the concept of generalized Bruck–Reilly extensions. We call a (right) type B ω−ω− semigroup with the generalized Bruck–Reilly extension a ∼ bisimple (right) type B ω−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−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.