Power cancellation of modules

Robert M. Guralnick

Vol. 124 (1986), No. 1, 131–144

DOI: 10.2140/pjm.1986.124.131

Abstract

It is shown that for R an integrally closed domain then M ⊕ X≅N ⊕ X implies M^(t)≅N^(t) for some positive integer t for all finitely generated S-modules M, N, X whenever S is a module finite algebra if and only if one is in the stable range of the integral closure of R in the algebraic closure of its quotient field. In particular, this holds whenever R is a Dedekind domain with all residue fields torsion. This extends work of Goodearl, who showed this holds for module finite (and more generally, finite rank) algebras over the integers.

Mathematical Subject Classification 2000

Primary: 16A53, 16A53

Secondary: 13C99, 13B20

Milestones

Received: 30 May 1984

Revised: 10 February 1985

Published: 1 September 1986