A note on two generalizations of QF − 3

Charles Irvin Vinsonhaler

Vol. 40 (1972), No. 1, 229–233

DOI: 10.2140/pjm.1972.40.229

Abstract

If M is an R-module, then the dual of M is defined to be Hom_R(M,R). Artinian QF-3 rings R have been characterized by the following two properties:

(1) The class of R-modules with zero duals is closed under taking submodules.

(2) The class of torsionless R-modules is closed under extension.

These properties are independent and, in the present paper, we study the two classes of rings R which satisfy each of these conditions separately.

Mathematical Subject Classification

Primary: 16A36

Milestones

Received: 27 January 1970

Published: 1 January 1972