2006•Journal of Lanzhou UniversityRequires access

Completely simple semigroup congruences on regular semigroup

Li Xiaoling

Abstract

The completely simple semigroup congruences on regular semigroup are investigated and some equivalent characterization of completely simple congruences is obtained.We prove that≤* is the least completely simple semigroup congruence on a regular semigroup,(≤∪≤~(-1))t is the least completely simple semigroup congruence on a locally inverse semigroup and the the least,group congruence on an inverse semigroup.

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Key concepts: Congruence relation, Cancellative semigroup, Semigroup, Bicyclic semigroup, Congruence (geometry), Mathematics, Inverse semigroup, Simple (philosophy)