数学
半群
换位(逻辑)
半群的特殊类
正则半群
纯数学
反向
订单(交换)
身份(音乐)
域代数上的
离散数学
几何学
物理
财务
经济
声学
作者
Xiaohong Zhang,Yudan Du
出处
期刊:Mathematics
[MDPI AG]
日期:2022-03-22
卷期号:10 (7): 1021-1021
被引量:7
摘要
Regular semigroups and their structures are the most wonderful part of semigroup theory, and the contents are very rich. In order to explore more regular semigroups, this paper extends the relevant classical conclusions from a new perspective: by transforming the positions of the elements in the regularity conditions, some new regularity conditions (collectively referred to as transposition regularity) are obtained, and the concepts of various transposition regular semigroups are introduced (L1/L2/L3, R1/R2/R3-transposition regular semigroups, etc.). Their relations with completely regular semigroups and left (right) regular semigroups, proposed by Clifford and Preston, are analyzed. Their properties and structures are studied from the aspects of idempotents, local identity elements, local inverse elements, subsemigroups and so on. Their decomposition theorems are proved respectively, and some new necessary and sufficient conditions for semigroups to become completely regular semigroups are obtained.
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