The group of units of a commutative semigroup ring

Robert William Gilmer, Jr. and Raymond Heitmann

Vol. 85 (1979), No. 1, 49–64

DOI: 10.2140/pjm.1979.85.49

Abstract

We seek a characterization, in terms of the coefficients and support of an element, of the units of the semigroup ring R[X;S], where R is a commutative ring with identity and S is an additive abelian semigroup with identity. Such a characterization requires some restrictions on the semigroup S.

We obtain results of the desired form in §2 for the case where S is torsion-free and cancellative, and in §3 under the weaker hypothesis that S is torsion-free and has no nonzero idempotents. Under this weaker hypothesis on S, the torsion subgroup of the group of units of R[X;S] is determined in §4 of this paper.

Mathematical Subject Classification 2000

Primary: 20M25

Milestones

Received: 29 November 1978

Published: 1 November 1979