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Prime rings for which the set of nonzero ideals is a special class

Published online by Cambridge University Press:  09 April 2009

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

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We show that the rings described in the title are precisely the indecomposable injectives for the category whose objects are the associative rings and 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.

Type
Research Article
Information
Journal of the Australian Mathematical Society , Volume 51 , Issue 1 , August 1991 , pp. 27 - 32
Copyright
Copyright © Australian Mathematical Society 1991

References

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