A characterization of QF − 3 rings

Edgar Andrews Rutter

Vol. 51 (1974), No. 2, 533–536

DOI: 10.2140/pjm.1974.51.533

Abstract

Let R be a ring with minimum condition on left or right ideals. It is shown that R is a QF ⋅ 3 ring if and only if each finitely generated submodule of the injective hull of R, regarded as a left R-module, is torsionless. The same approach yields a simplified proof that R is quasi-Frobenius if and only if every finitely generated left R-module is torsionless.

Mathematical Subject Classification

Primary: 16A36

Milestones

Received: 1 February 1973

Published: 1 April 1974