TY - JOUR
T1 - Transfer of Gorenstein dimensions along ring homomorphisms
AU - Christensen, Lars Winther
AU - Sather-Wagstaff, Sean
PY - 2010/6
Y1 - 2010/6
N2 - 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.
AB - 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.
UR - http://www.scopus.com/inward/record.url?scp=74149087197&partnerID=8YFLogxK
U2 - 10.1016/j.jpaa.2009.09.007
DO - 10.1016/j.jpaa.2009.09.007
M3 - Article
AN - SCOPUS:74149087197
VL - 214
SP - 982
EP - 989
JO - Journal of Pure and Applied Algebra
JF - Journal of Pure and Applied Algebra
SN - 0022-4049
IS - 6
ER -