This paper provides a method to get a noetherian local UFD with an isolated singularity from
a given noetherian local ring, preserving certain properties, which is applied to invesitgate …

For finitely generated modules $ M $ and $ N $ over a commutative Noetherian local ring $
R $, we give various sufficient criteria for detecting freeness of $ M $ or $ N $ via vanishing …

We find necessary and sufficient conditions for a complete local ring to be the completion of
a noncatenary local (Noetherian) domain, as well as necessary and sufficient conditions for …

Let $ R $ be a commutative noetherian local ring, and let $ M $ be a finitely generated $ R $-
module. Inspired by works of Vasconcelos and Briggs on characterization of complete …

Let $ M $ be a non-zero finitely generated module over a finite dimensional commutative
Noetherian local ring $(R,\mathfrak {m}) $ with dim $ _R (M)= t $. Let $ I $ be an ideal of $ R …

Given a commutative Noetherian ring $ R $ with total ring of fractions $ Q (R) $, and a finitely
generated $ R $-submodule $ M $ of $ Q (R) $, we prove an equality between trace ideal …

In this paper we prove a finiteness result for infinite minimal free resolutions over a
Noetherian local ring R: If M is a module, such as the residue field, that is locally free of …

Let R be a commutative noetherian local ring and consider the set of isomorphism classes of
indecomposable totally reflexive R-modules. We prove that if this set is finite, then either it …

Throughout, R is a commutative Noetherian ring with non-zero identity, a is an ideal of R, M
is a finite (ie, finitely generated) R-module, and n is a non-negative integer. For basic results …

We prove two theorems on the vanishing of Ext over commutative Noetherian local rings.
Our first theorem shows that, over non-regular Cohen-Macaulay local domains, there are no …