Vol. 24, No. 1, 1968

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Hypercyclic rings

William Howard Caldwell

Vol. 24 (1968), No. 1, 29–44
Abstract

The object of this paper is to provide characterizations for certain rings R having the property that each cyclic right R-module has a cyclic injective hull.1 Such rings will be called hypercyclic. Characterizations for left perfect hypercyclic rings and commutative hypercyclic rings are given in terms of their ideal structure and self-injectivity. An example of a commutative hypercyclic ring without chain conditions is given to demonstrate that the characterization obtained is nontrivial.

Mathematical Subject Classification
Primary: 16.50
Milestones
Received: 8 December 1966
Published: 1 January 1968
Authors
William Howard Caldwell