Regular semigroup

Regular semigroup

A regular semigroup is a semigroup where all elements are regular (completely regular), meaning that for every element there exists an idempotent element that is a lower bound for all elements in its class. Additionally, if a regular semigroup is inverse, then each class and each class of S contains a unique idempotent.From: Electronics, Communications and Networks IV [2015], A new characterization of fuzzy ideals of semigroups and its applications [2021]

On certain transformation semigroups

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Published in Amir Hussain, Mirjana Ivanovic, Electronics, Communications and Networks IV, 2015

Jia Zhang

An element a of a semigroup S is regular [completely regular] if a=axa[a=axa and ax=xa] for some x∈S. If all the elements of S are regular [completely regular], we say that S is a regular semigroup [completely regular semigroup]. Regular semigroup is a special class of semigroups which are particular amenable to be analyzed by using Green's relations. Completely regular semigroup is a special class of regular semigroups. The more other related information, the reader is referred to Petrich (Petrich & Reilly 1999). In this section, we first characterize the regular elements and completely regular elements of F(M). Then we give a sufficient and necessary condition under which F(M) is regular and completely regular. We first need some results that will be used later.

A new characterization of fuzzy ideals of semigroups and its applications

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Published in Automatika, 2021

Chunhua Li, Baogen Xu, Huawei Huang

Note that a regular semigroup S is inverse if each class and each class of S contains a unique idempotent. As an immediate corollary of Corollary 5.1 and Theorem 4.4, we have

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On certain transformation semigroups

A new characterization of fuzzy ideals of semigroups and its applications