We introduce the notion of Burch submodules and weakly m-full submodules of modules
over a local ring (R, m) and study their properties. One of our main results shows that Burch …

For a finitely generated module M over a commutative Noetherian ring R, we settle the
Auslander–Reiten conjecture when at least one of Hom R (M, R) and Hom R (M, M) has …

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 …

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 study a modified version of the classical Ulrich modules, which we call $ c $-Ulrich.
Unlike the traditional setting, $ c $-Ulrich modules always exist. We prove that these …

We address the problem of when the tensor product of two finitely generated modules over a
Cohen-Macaulay local ring is Ulrich in the generalized sense of Goto et al., and in particular …

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 …

Over a commutative Noetherian ring, we show that Auslander-Reiten conjecture holds true
for the class of (finitely generated) modules whose dual has finite complete intersection …