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Self-injective rings

Published:1979 Issue:2 Volume:77 Page:157-164
ISSN:0002-9939
Container-title:Proceedings of the American Mathematical Society
language:en
Short-container-title:Proc. Amer. Math. Soc.

Author:

Faith Carl

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 = E n d A E B = \mathrm {End}_A E is commutative. In this case B = End B E B = \text {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.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Link

http://www.ams.org/proc/1979-077-02/S0002-9939-1979-0542077-8/S0002-9939-1979-0542077-8.pdf

Reference30 articles.

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2. Completely faithful modules and self-injective rings;Azumaya, Goro;Nagoya Math. J.,1966

3. Die Grundlehren der mathematischen Wissenschaften, Band 190;Faith, Carl,1973

4. Grundlehren der Mathematischen Wissenschaften, No. 191;Faith, Carl,1976

5. Injective cogenerator rings and a theorem of Tachikawa;Faith, Carl;Proc. Amer. Math. Soc.,1976

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