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| Paper IPM / M / 8341 |
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| Abstract: | |||||
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\Ext-finite modules were introduced and studied by
Enochs and Jenda. We prove under some conditions that the depth of a
local ring is equal to the sum of the Gorenstein injective dimension
and \Tor-\depth of an \Ext-finite module of finite Gorenstein
injective dimension. Let (R,\fm) be a local ring. We say that an
R-module M with dimR M=n is a Grothendieck module if
the n-th local cohomology module of M with respect to \fm,
\"\fm n (M), is non-zero. We prove the Bass formula for this
kind of modules of finite Gorenstein injective dimension and of
maximal Krull dimension. These results are dual versions of the
Auslander-Bridger formula for the Gorenstein dimension. We also
introduce GF-perfect modules as an extension of quasi-perfect
modules introduced by Foxby.
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