Finite dimensional torsion free rings

Thomas J. Cheatham

Vol. 39 (1971), No. 1, 113–118

DOI: 10.2140/pjm.1971.39.113

Abstract

In the class of rings with zero singular left ideal, several characterizations of rings with finite left Goldie dimension are given. They include: the direct limit of torsion free modules is torsion free; the direct limit of torsion free injective modules is injective; each absolutely pure torsion free module is injective; each module has a unique (up to isomorphism) torsion free covering module. The latter result gives a converse, in a special case, to a theorem of Mark Teply.

Mathematical Subject Classification

Primary: 16A64

Milestones

Received: 2 April 1971

Revised: 15 July 1971

Published: 1 October 1971