Hermite semigroup rings

Leo George Chouinard, II

Vol. 101 (1982), No. 1, 25–39

DOI: 10.2140/pjm.1982.101.25

Abstract

If S is a commutative, separative semigroup with identity, and R is a commutative ring with unit such that R[S] is arithmetical, then a local-global principle for verifying algebraic equations in R[S] is established. This is then used to show that if S is not a union of torsion groups, then R[S] is an elementary divisor ring.

Mathematical Subject Classification 2000

Primary: 20M25

Secondary: 13F99, 16A78

Milestones

Received: 5 June 1980

Published: 1 July 1982