Algebras for which every indecomposable right module is invariant in its injective envelope

Spencer Ernest Dickson and Kent Ralph Fuller

Vol. 31 (1969), No. 3, 655–658

DOI: 10.2140/pjm.1969.31.655

Abstract

The algebras of the title are characterized as those having Tachikawa’s strong left cyclic representation type (SLCRT) with the further property that every quotient of a principal indecomposable left module has square free socle. Moreover it turns out that these are precisely the algebras for which every indecomposable right module is quasi-injective in the sense of Johnson and Wong, and that these algebras have finite module type.

Mathematical Subject Classification

Primary: 16.40

Milestones

Received: 11 October 1968

Published: 1 December 1969