Vol. 39, No. 1, 1971

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Finite dimensional torsion free rings

Thomas J. Cheatham

Vol. 39 (1971), No. 1, 113–118

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
Received: 2 April 1971
Revised: 15 July 1971
Published: 1 October 1971
Thomas J. Cheatham