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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Self-injective rings


Author: Carl Faith
Journal: Proc. Amer. Math. Soc. 77 (1979), 157-164
MSC: Primary 16A52
MathSciNet review: 542077
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Abstract: In 1958 Matlis proved that the study of Noetherian complete local rings could be subsumed under the study of injective modules E over a commutative ring A such that $ B = \mathrm{End}_A E$ is commutative. In this case $ B =$   End$ _B E$, and E is said to be strongly balanced over B. The main theorem of this paper shows that the study of strongly balanced injectives over any ring, and hence the study of Monta self-dualities, is contained in the study of self-injective rings.


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DOI: http://dx.doi.org/10.1090/S0002-9939-1979-0542077-8
PII: S 0002-9939(1979)0542077-8
Article copyright: © Copyright 1979 American Mathematical Society