A structure theorem of left regular cyber-groups

Year 2017, Volume: 46 Issue: 6, 1093 - 1104, 01.12.2017

Ying Yuan Xueming Ren K. P. Shum

Abstract

An abundant semigroup S is a superabundant semigroup if each $\mathcal{H}^*$-class of S contains an idempotent. We call a superabundant semigroup a left regular cyber-group if the set of its idempotents forms a left regular band. After the investigation of the properties of superabundant semigroups, we establish a structure theorem for the left regular cybergroups by using the newly defined left twist product of semigroups.

Keywords

Completely regular semigroups, Superabundant semigroups, Left regular cyber-groups

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