J Austral Math Soc Ser A 51 pp27--32, 1991.

Prime Rings for which the Set of Nonzero Ideals is a Special Class

B. J. Gardner

(Received 13 February 1989; revised 31 August 1989)

Abstract

We show that the rings described in the title are precisely the indecomposable injectives for the category whose objects are the assiciative rings whose morphisms are the ring homomorphisms with accessible images. These rings are more or less completely known. Those of cardinality greater than that of the continuum are subdirectly irreducible but there are some nontrivial principal ideal domains in the class.

1980 AMS Subject Classification (1985 Revision): 16A21

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Authors

B. J. Gardner: Department of Mathematics, University of Tasmania, G.P.O. Box 252C, Hobart Tasmania 7001, Australia.

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Last Modified: Mon Feb 3 9:46:10 2003