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Zapiski Nauchnykh Seminarov POMI, 1999, Volume 265, Pages 169–188
(Mi znsl1196)
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Local duality for modules over Noetherian commutative rings
M. B. Zvyagina Saint-Petersburg State University
Abstract:
Some applications of the general theorem on the existence of local duality for modules over Noetherian commutative rings are given.
Let $\Lambda$ be a Noetherian commutative ring, let $\mathscr M=\{\mathfrak M\}$ be a set of maximal ideals in $\Lambda$, and let $\widehat\Lambda=\varprojlim\Lambda_\mathfrak M$, $\Gamma(\Lambda)=\prod\limits_{\mathfrak M\in\mathscr M}\widehat\Lambda_\mathfrak M$. Then the category of Artin modules is dual to the category of Noetherian modules.
Several structural results are proved including the theorem of the structure of Artin modules over principal ideal
domains. For rings of special kinds, theorems on double centralizers are proved.
Received: 21.11.1999
Citation:
M. B. Zvyagina, “Local duality for modules over Noetherian commutative rings”, Problems in the theory of representations of algebras and groups. Part 6, Zap. Nauchn. Sem. POMI, 265, POMI, St. Petersburg, 1999, 169–188; J. Math. Sci. (New York), 112:4 (2002), 4337–4347
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https://www.mathnet.ru/eng/znsl1196 https://www.mathnet.ru/eng/znsl/v265/p169
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