Commutative cancellative semigroups without idempotents
Howard B. Hamilton, THOMAS E. NORDAHL, Takayuki Tamura · Pacific Journal of Mathematics · 1975
A commutative cancellative idempotent-free semigroup (CCIF-) S can be described in terms of a commutative cancellative semigroup C with identity, an ideal of C, and a function of C X C into integers.If C is an abelian group, S has an archimedean component as an ideal; S is called an ^-semigroup.A CCIF-semigroup of finite rank has nontrivial homomorphism into nonnegative real numbers.