21 research outputs found
Exceptional Sequences over Graded Cohen-Macaulay Rings
The concept of exceptional sequences was developed by Gorodentsev and Rudakov in [3] and generalized by Bondal in [1]. It is a crucial tool to classify exceptional modules over hereditary algebras and exceptiona
A Homological dimension related to AB rings
There are many homological dimensions which are closely related to ring
theoretic properties. The notion of a AB ring has been introduced by Huneke and
Jorgensen. It has nice homological properties. In this paper, we shall define a
homological dimension which is closely related to a AB ring, and investigate
its properties.Comment: 7page
A Characterization of One Dimensional N-Graded Gorenstein Rings of Finite Cohen-Macaulay Representation Type
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