Residuated Completely Simple Semigroups

• 作者: G.A. Pinto T.S. Blyth
• 来源期刊: 代数集刊:英文版
• 学科: 数学
• 关键词: 完全单半群 剩余半群 最大幂等元 字典顺序 循环群 X-1 单产量 等幂和
• 年，卷（期）: 2014,（2）
• 页码范围: 181-194
• 页数: 14页
• 分类号: O152.7
• 语种: 中文

摘要

We consider particular compatible orders on a given completely simple semi- group Sx= M((x); I, A; P) where (x) is an ordered cyclic group with x 〉 1 and p11= x-1. Of these, only the lexicographic and bootlace orders yield residuated semigroups. With the lexicographic order, Sx is orthodox and has a biggest idempotent. With the bootlace order, the maximal idempotents of Sx are identified by specific locations in the sandwich matrix. In the orthodox case there is also a biggest idempotent and, for sandwich matrices of a given size, uniqueness up to ordered semigroup isomorphism is established.