Vol. 75, No. 2, 1978

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Congruences on N-semigroups

H. B. Hamilton

Vol. 75 (1978), No. 2, 423–448

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

Mathematical Subject Classification 2000
Primary: 20M15
Secondary: 20M11
Received: 29 April 1976
Revised: 24 March 1977
Published: 1 April 1978
H. B. Hamilton