N-Congruences of N-semigroups

AbstractBy an N-semigroup we mean a commutative archimedean cancellative semigroup without idempotent. A congruence ϱ on an N-semigroup S is called an N-congruence on S if S/g9 is an N-semigroup. This paper discusses how to determine N-congruences on S in the two ways. There is a maximal N-congruence ϱ0 on S. S/ϱ0 is an irreducible N-semigroup. Every N-semigroup is isomorphic to a subdirect product of an irreducible N-semigroup and an abelian group