Gorenstein dimension of modules over homomorphisms

Details Gorenstein dimension of modules over homomorphisms Gorenstein dimension of modules over homomorphisms

2005-04-16

arxiv.org/abs/math/0504340v2

Mathematics

Commutative Algebra

14 pp. To appear in J. Pure Appl. Algebra. Also available from http://www.math.unl.edu/~lchristensen3/index.html

Scientific paper

Given a homomorphism of commutative noetherian rings R --> S and an S-module N, it is proved that the Gorenstein flat dimension of N over R, when finite, may be computed locally over S. When, in addition, the homomorphism is local and N is finitely generated over S, the Gorenstein flat dimension equals sup{m | Tor^R_m(E,N) \noteq 0} where E is the injective hull of the residue field of R. This result is analogous to a theorem of Andr\'e on flat dimension.

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