|
|||||
|
|
|
|
|
|
|
|
|
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 | |
|
