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.
