Vol. 61, No. 2, 1975

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Commutative cancellative semigroups without idempotents

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

Vol. 61 (1975), No. 2, 441–456

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
Received: 19 March 1975
Published: 1 December 1975
H. B. Hamilton
T. E. Nordahl
Takayuki Tamura