Vol. 31, No. 3, 1969

Download this article
Download this article. For screen
For printing
Recent Issues
Vol. 294: 1
Vol. 293: 1  2
Vol. 292: 1  2
Vol. 291: 1  2
Vol. 290: 1  2
Vol. 289: 1  2
Vol. 288: 1  2
Vol. 287: 1  2
Online Archive
Volume:
Issue:
     
The Journal
Subscriptions
Editorial Board
Officers
Special Issues
Submission Guidelines
Submission Form
Contacts
Author Index
To Appear
 
ISSN: 0030-8730
Rings in which minimal left ideals are projective

Robert Fred Gordon

Vol. 31 (1969), No. 3, 679–692
Abstract

Let R be an associative ring with identity. Then the left socle of R is a direct summand of R as a right R-module if and only if it is projective as a left R-module and contains no infinite sets of orthogonal idempotents. This implies, for example, that a ring with finitely generated left socle and no nilpotent minimal left ideals is a ring direct sum of a semisimple artinian ring and a ring with zero left socle.

Mathematical Subject Classification
Primary: 16.50
Milestones
Received: 15 November 1968
Revised: 26 June 1969
Published: 1 December 1969
Authors
Robert Fred Gordon