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Paper   IPM / M / 8341
School of Mathematics
  Title:   Dual of the Auslander-Bridger formula and GF-perfectness
1.  T. Sharif
2.  P. Sahandi
  Status:   Published
  Journal: Math. Scand.
  Vol.:  101
  Year:  2007
  Pages:   5-18
  Supported by:  IPM
\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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