Transfer of Gorenstein dimensions along ring homomorphisms

Abstract

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.

Removed section 2. Final version; to appear in J. Pure Appl. Algebra, 12 pp. Also available from the authors' homepages http://www.math.ttu.edu/~lchriste/publications.html and http://www.math.ndsu.nodak.edu/faculty/ssatherw/research.html