Modules of finite homological dimension with respect to a semidualizing module Page 1
Arch. Math. 93 (2009), 111–121 c© 2009 Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020111-11 …

Let R and S be rings and RCS a semidualizing bimodule. We show that the supremum of the
C-projective dimensions of C-flat left R-modules is less than or equal to that for left R …

Cohen-Macaulay dimension for modules over a commutative ring has been defined by AA
Gerko. That is a homological invariant sharing many properties with projective dimension …

A generalization of a theorem of Foxby Page 1 Arch. Math. 93 (2009), 123–127 c© 2009
Birkhäuser Verlag Basel/Switzerland 0003-889X/09/020123-5 published online August 6, 2009 …

We obtain various characterizations of commutative Noetherian local rings (R, m) in terms of
homological dimensions of certain finitely generated modules. Our argument has a series of …

A question of Avramov and Foxby concerning injective dimension of complexes is settled in
the affirmative for the class of noetherian rings. A key step in the proof is to recast the …

A new homological dimension, called G*-dimension, is defined for every finitely generated
module M over a local noetherian ring R. It is modeled on the CI-dimension of Avramov …

New homotopy invariant finiteness conditions on modules over commutative rings are
introduced, and their properties are studied systematically. A number of finiteness results for …

If M is a nonzero finitely generated module over a commutative Noetherian local ring R such
that M has finite injective dimension and finite Gorenstein dimension, then it follows from a …

A semi-dualizing module over a commutative noetherian ring A is a finitely generated
module C with RHomA (C, C)≃ A in the derived category D (A). We show how each such …