Projective ideals in rings of dimension one

On Residually S2 Ideals and Projective Dimension One Modules

We prove that certain modules are faithful. This enables us to draw consequences about the reduction number and the integral closure of some classes of ideals.

Ideals with larger projective dimension and regularity

We define a family of homogeneous ideals with large projective dimension and regularity relative to the number of generators and their common degree. This family subsumes and improves upon constructions given in [Cav04] and [McC]. In particular, we describe a family of three-generated homogeneous ideals in arbitrary characteristic whose projective dimension grows

Fitting Ideals and Finite Projective Dimension

Throughout we let (T,m, k) denote a commutative Noetherian local ring with maximal ideal m and residue field k. We let I ⊆ T be an ideal generated by a regular sequence of length c and set R := T/I. In the important paper [A], Avramov addresses the following question. Given a finitely generated R-module M , when does M have finite projective dimension over a ring of the form T/J , where J is ge...

Some Ideals with Large Projective Dimension

For an ideal I in a polynomial ring over a field, a monomial support of I is the set of monomials that appear as terms in a set of minimal generators of I. Craig Huneke asked whether the size of a monomial support is a bound for the projective dimension of the ideal. We construct an example to show that, if the number of variables and the degrees of the generators are unspecified, the projectiv...

On One-Sided Ideals of Rings of Linear Transformations