TY - JOUR
T1 - Gorenstein dimension of modules over homomorphisms
AU - Christensen, Lars Winther
AU - Iyengar, Srikanth
N1 - Funding Information:
We thank Lucho Avramov and Sean Sather-Wagstaff for their comments and suggestions on this work. L.W.C. was partly supported by a grant from the Danish Natural Science Research Council. S.I. was partly supported by NSF grant DMS 0442242.
PY - 2007/1
Y1 - 2007/1
N2 - 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 ∈ Z {divides} TormR (E, N) ≠ 0}, where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension.
AB - 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 ∈ Z {divides} TormR (E, N) ≠ 0}, where E is the injective hull of the residue field of R. This result is analogous to a theorem of André on flat dimension.
UR - http://www.scopus.com/inward/record.url?scp=33750459404&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2005.12.005
DO - 10.1016/j.jpaa.2005.12.005
M3 - Article
AN - SCOPUS:33750459404
SN - 0022-4049
VL - 208
SP - 177
EP - 188
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
IS - 1
ER -