On ∼ bisimple right type B ω− semigroups as model of some fractal structure. (August 2016)

• Record Type: Journal Article
• Authors: Li, Chunhua; Wang, Li-min; Xu, Baogen; Huang, Huawei
• Is Part Of: Chaos, solitons and fractals. Volume 89(2016)
• Page Start: 169
• Page End: 174
• Publication Date: 2016-08
• Subjects: ∼ bisimple -- Bruck–Reilly extensions -- (right) type B semigroups -- (left) good congruences -- ω− chains; Chaotic behavior in systems -- Periodicals; Solitons -- Periodicals; Fractals -- Periodicals; Chaotic behavior in systems; Fractals; Solitons; Periodicals; 003.7
• DOI: 10.1016/j.chaos.2015.10.022
• Languages: English
• ISSNs: 0960-0779

Abstract

Abstract: 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.