In this paper, sufficient conditions for finitely generated modules over a commutative
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …

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 …

We provide a duality theorem between Ext and Tor modules over a Cohen-Macaulay local
ring possessing a canonical module, and use it to prove some freeness criteria for finite …

This work is about some features of local cohomology theory. We develop a new tool called
Mayer-Vietoris spectral sequence that allows us to study several local cohomology modules …

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 …

Let $(R,\mathfrak {m}, k) $ be a Noetherian local ring and let $ M $ be a finitely generated $
R $-module. The main focus of this paper is to give positive answers for some long-standing …

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 …

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 …

In this paper we give several classes of Non-Gorenstein local rings $ A $ which satisfy the
property that $\text {Ext}^ i_A (M, A)= 0$ for $ i\gg 0$ then $\text {projdim} _A M $ is finite. We …

arXiv:2404.02005v1 [math.AC] 2 Apr 2024 Page 1 arXiv:2404.02005v1 [math.AC] 2 Apr 2024
HOMOLOGY OF CONDUCTOR MOHSEN ASGHARZADEH ABSTRACT. We study some …