202 research outputs found
Stable degenerations of Cohen-Macaulay modules
As a stable analogue of degenerations, we introduce the notion of stable
degenerations for Cohen-Macaulay modules over a Gorenstein local algebra. We
shall give several necessary and/or sufficient conditions for the stable
degeneration. These conditions will be helpful to see when a Cohen-Macaulay
module degenerates to another.Comment: 29 pages, to appear in Journal of Algebr
Abstract local cohomology functors
We propose to define the notion of abstract local cohomology functors. The
derived functors of the ordinary local cohomology functor with support in the
closed subset defined by an ideal and the generalized local cohomology functor
associated with a given pair of ideals are characterized as elements of the set
of all the abstract local cohomology functors.Comment: To appear in Mathematical Journal of Okayama Universit
Upper Cohen-Macaulay Dimension
In this paper, we define a homological invariant for finitely generated modules over a commutative noetherian local ring, which we call upper Cohen-Macaulay dimension. This invariant is quite similar to Cohen-Macaulay dimension that has been introduced by Gerko. Also we
define a homological invariant with respect to a local homomorphism of local rings. This invariant links upper Cohen-Macaulay dimension with Gorenstein dimension.</p
Homological invariants associated to semi-dualizing bimodules
Cohen-Macaulay dimension for modules over a commutative noetherian local ring
has been defined by A. A. Gerko. That is a homological invariant sharing many
properties with projective dimension and Gorenstein dimension. The main purpose
of this paper is to extend the notion of Cohen-Macaulay dimension for modules
over commutative noetherian local rings to that for bounded complexes over
non-commutative noetherian rings.Comment: 19 pages, to appear in J. Math. Kyoto Uni
- …