Congruences on ∼ bisimple right type B ω – semigroups

Abstract

The structure of a ∼ bisimple right type B ω – semigroup was described by Li, Wang, Xu and Huang as the generalized Bruck-Reilly extensions. As a continuation of their work, in this paper, we shall consider some classes of congruences on such semigroups. It is shown that an arbitrary right * congruence on some classes of ∼ bisimple right type B ω – semigroups is either an idempotent-separating congruence or a left cancellative congruence.

Keywords:

• right type B semigroups
• idempotent-separating
• right * congruences
• ω – chains

AMS Mathematics Subject Classification(2010):

• 20M10
• 06F05