Self-injective rings

Faith, Carl

doi:10.1090/S0002-9939-1979-0542077-8

Self-injective rings
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Proc. Amer. Math. Soc. 77 (1979), 157-164 Request permission

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 $B = \text {End}_B E$, 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.

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