Dual of the Auslander-Bridger formula and GF-perfectness

• Autores: Parviz Sahandi, Tirdad Sharif
• Localización: Mathematica scandinavica, ISSN 0025-5521, Vol. 101, Nº 1, 2007, págs. 5-18
• Idioma: inglés
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• Resumen

  • 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 dimRM=n is a Grothendieck module if the n-th local cohomology module of M with respect to m, Hnm(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.