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Paper IPM / M / 8341  


Abstract:  
\Extfinite 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 \Extfinite module of finite Gorenstein
injective dimension. Let (R,\fm) be a local ring. We say that an
Rmodule M with dim_{R} M=n is a Grothendieck module if
the nth local cohomology module of M with respect to \fm,
\"_{\fm} ^{n} (M), is nonzero. 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
AuslanderBridger formula for the Gorenstein dimension. We also
introduce GFperfect modules as an extension of quasiperfect
modules introduced by Foxby.
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