Structure of Strict Abundant Semigroups

• 来源期刊: 代数集刊（英文版）
• 关键词: structure regular semigroup strict regular semigroup abundant semigroup strict abundant semigroup
• 年，卷（期）: 2019,（3）
• 页码范围: 387-400
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386719000282

摘要

We introduce a new class of semigroups called strict abundant semigroups,which are concordant semigroups and subdirect products of completely (J)*-simple abundant semigroups and completely 0-(J)*-simple primitive abundant semigroups.A general construction and a tree structure of such semigroups are established.Consequently,the corresponding structure theorems for strict regular semigroups given by Auinger in 1992 and by Grillet in 1995 are generalized and extended.Finally,an example of strict abundant semigroups is also given.