Commutative cancellative semigroups without idempotents

H. B. Hamilton, T. E. Nordahl and Takayuki Tamura

Vol. 61 (1975), No. 2, 441–456

DOI: 10.2140/pjm.1975.61.441

Abstract

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 × C into integers. If C is an abelian group, S has an archimedean component as an ideal; S is called an N-semigroup. A CCIF-semigroup of finite rank has nontrivial homomorphism into nonnegative real numbers.

Mathematical Subject Classification 2000

Primary: 20M10

Milestones

Received: 19 March 1975

Published: 1 December 1975