Congruences on N-semigroups
Howard B. Hamilton · Pacific Journal of Mathematics · 1978
The study of a semigroup in terms of its congruence relations has been used many times in the past.In the case of ^-semigroups Tamura initiated this study with a paper [9] determining the ^-congruences of an ^-semigroup.Recently, Dickinson [4] has determined the congruences which correspond to homomorphic images having no idempotents as refinements of 9?-congruences.Group congruences on a commutative semigroup have been determined by Tamura and the author [11], but here they are determined for an ^-semigroup from the group of quotients of the ^-semigroup, ^-congruences and group congruences on ^-semigroups are of fundamental importance in characterizing ^-semigroups.In this paper we make a study of all types of congruences on ^-semigroups.