We analyze whether Ulrich modules, not necessarily maximal CM (Cohen-Macaulay), can
be used as test modules, which detect finite homological dimensions of modules. We prove …

A conjecture of Huneke and Wiegand claims that, over one-dimensional commutative
Noetherian local domains, the tensor product of a finitely generated, non-free, torsion-free …

A celebrated conjecture of Auslander and Reiten claims that a finitely generated module M
that has no extensions with M⊕ Λ over an Artin algebra Λ must be projective. This …

The notion of Burch ideals and Burch submodules were introduced (and studied) by Dao-
Kobayashi-Takahashi in 2020 and Dey-Kobayashi in 2022 respectively. The aim of this …

We show that every integrally closed m-primary ideal I in a commutative Noetherian local
ring (R, m, k) has maximal complexity and curvature, ie, cx R (I)= cx R (k) and curv R (I)= curv …

Motivated by the notion of geometrically linked ideals, we show that over a Gorenstein local
ring R, if a Cohen-Macaulay R-module M of grade g is linked to an R-module N by a …

In this paper, we are concerned with the following question: if the tensor product of finitely
generated modules M and N over a local complete intersection domain is maximal Cohen …

We discuss a class of modules, called test modules, that are, in principle, those detecting
finite homological dimensions. The main purpose of this mote is to report the following result …