A structure theorem of left regular cyber-groups

Authors : Ying YUAN, Xueming REN, K. P. SHUM

Pages : 1093-1104

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Publication Date : 2017-12-01

Article Type : Research Paper

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