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.
Cite
@article{arxiv.0807.0706,
title = {Transfer of Gorenstein dimensions along ring homomorphisms},
author = {Lars Winther Christensen and Sean Sather-Wagstaff},
journal= {arXiv preprint arXiv:0807.0706},
year = {2009}
}
Comments
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