Commutative cancellative semigroups with nontrivial homomorphisms into nonnegative real numbers

Abstract

Let S be a commutative Cancellative semigroup. Under what condition on S is S nontrivially homomorphic into the nonnegative (positive) real number additive semigroup? The question was answered in the special cases [1, 3]. In this paper the author gives necessary and sufficient conditions in the general case from the various points of view: embeddings, partial orderings, the system of ideals, B -condition and structure semigroups.