On Superabundant Semigroups Whose Set of Idempotents Forms a Subsemigroup

• 来源期刊: 代数集刊（英文版）
• 关键词: cyber-groups orthogroups superabundant semigroups rectangular monoids left C-a semigroups
• 年，卷（期）: 2007,（2）
• 页码范围: 215-228
• 页数: 14页
• 语种: 英文

摘要

In this paper, we study the structure of a superabundant semigroup S whose set of idempotents E(S) forms a subsemigroup.We call such a semigroup a cyber-group because it is a generalization of orthogroups in the class of completely regular semigroups studied by Petrieh and ReillyWe show that a cyber-group can be expressed as a semilattice of rectangular monoidsThus, our result generalizes the well-known result obtained by Petrich in 1987 for orthogroupsSome properties of cyber-groups are given and some special superabundant semigroups are discussed.