Vol. 40, No. 1, 1972

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A note on two generalizations of QF 3

Charles Irvin Vinsonhaler

Vol. 40 (1972), No. 1, 229–233

If M is an R-module, then the dual of M is defined to be HomR(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
Received: 27 January 1970
Published: 1 January 1972
Charles Irvin Vinsonhaler