We construct a local Cohen–Macaulay ring R with a prime ideal p∈ Spec (R) such that R
satisfies the uniform Auslander condition (UAC), but the localization R p does not satisfy …

Let R be a Cohen–Macaulay local ring. In this paper, we study the structure of Ulrich R-
modules mainly in the case where R has minimal multiplicity. We explore generation of …

Let $(R,\underline {m}) $ be a commutative Noetherian local ring and $ M $ be a non-zero
finitely generated $ R $-module. We show that if $ R $ is almost Cohen-Macaulay and $ M …

Let (R, m) be a Cohen–Macaulay local ring of dimension d, C a canonical R-module and M
an almost Cohen–Macaulay R-module of dimension n and of depth t. We prove that dim Ext …

Let $(R,\frak m) $ be a homomorphic image of a Cohen-Macaulay local ring and $ M $ a
finitely generated $ R $-module. We use the splitting of local cohomology to shed a new light …

Let (R, m) be a relative Cohen–Macaulay local ring with respect to an ideal a of R and set c
to be ht a. We investigate some properties of the Matlis dual of the R-module H ac (R), and …

We investigate properties of certain invariants of Noetherian local rings, including their
behavior under flat local homomorphisms. We show that these invariants are bounded by …

Let R be a Cohen–Macaulay local ring possessing a canonical module. In this paper, we
consider when the maximal ideal of R is self-dual—ie, it is isomorphic to its canonical dual …

A commutative Noetherian local ring $(R,\mathfrak m, k) $ is called Dedekind-like provided $
R $ is one-dimensional and reduced, the integral closure $\overline {R} $ is generated by at …

We study the duality for maximal Cohen-Macaulay modules (MCM modules for short) over
Cohen-Macaulay local rings. We characterize (low dimensional) rings over which any MCM …