Vol. 31, No. 3, 1969

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Rings in which minimal left ideals are projective

Robert Fred Gordon

Vol. 31 (1969), No. 3, 679–692

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
Received: 15 November 1968
Revised: 26 June 1969
Published: 1 December 1969
Robert Fred Gordon