Vol. 39, No. 1, 1971

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 328: 1  2
Vol. 327: 1  2
Vol. 326: 1  2
Vol. 325: 1  2
Vol. 324: 1  2
Vol. 323: 1  2
Vol. 322: 1  2
Vol. 321: 1  2
Online Archive
The Journal
About the journal
Ethics and policies
Peer-review process
Submission guidelines
Submission form
Editorial board
ISSN: 1945-5844 (e-only)
ISSN: 0030-8730 (print)
Special Issues
Author index
To appear
Other MSP journals
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