Transfer of Gorenstein dimensions along ring homomorphisms

Details Transfer of Gorenstein dimensions along ring homomorphisms Transfer of Gorenstein dimensions along ring homomorphisms

2008-07-04

arxiv.org/abs/0807.0706v4

Mathematics

Commutative Algebra

Removed section 2. Final version; to appear in J. Pure Appl. Algebra, 12 pp. Also available from the authors' homepages http

Scientific paper

A central problem in the theory of Gorenstein dimensions over commutative noetherian rings is to find resolution-free characterizations of the modules for which these invariants are finite. Over local rings, this problem was recently solved for the Gorenstein flat and the Gorenstein projective dimensions; here we give a solution for the Gorenstein injective dimension. Moreover, we establish two formulas for the Gorenstein injective dimension of modules in terms of the depth invariant; they extend formulas for the injective dimension due to Bass and Chouinard.

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