Dual of the Auslander-Bridger formula and GF-perfectness - Sahandi, Parviz; Sharif, Tirdad (MATHEMATICA SCANDINAVICA, 2007)
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,m) be a local ring. We say that an R-module M with _R M=n is a Grothendieck module if the n-th local cohomology module of M with respect to m, H_m^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.