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 …

Auslander-Reiten Conjecture for commutative Noetherian rings predicts that a finitely
generated module is projective when certain Ext-modules vanish. But what if those Ext …

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 …

arXiv:2312.06124v1 [math.AC] 11 Dec 2023 Page 1 arXiv:2312.06124v1 [math.AC] 11 Dec
2023 SOME RESULTS ON VANISHING OF EXT AND FINITE GORENSTEIN DIMENSION OF …

ON ONE-DIMENSIONAL LOCAL RINGS AND BERGER’S CONJECTURE Page 1 Proceedings
of the Edinburgh Mathematical Society (2023) 66, 437–452 doi:10.1017/S0013091523000214 …

The aim of this article is to consider the spectral sequences induced by tensor-hom
adjunction, and provide a number of new results. Let R be a commutative Noetherian local …

Let $(R,\fm) $ be a local ring, and let $ C $ be a semidualizing complex. We establish the
equality $ r_R (Z)=\nu (\Ext^{g-\inf C} _R (Z, C))\mu^{\depth C} _R (\mathfrak {m}, C) $ for a …

It is well-known that the generalized Auslander-Reiten condition (GARC) and the symmetric
Auslander condition (SAC) are equivalent, and (GARC) implies that the Auslander-Reiten …

Let $ R $ be a Noetherian local ring, and let $ C $ be a semidualizing $ R $-module. In this
paper, we present some results concerning to vanishing of $\operatorname {Ext} $ and finite …

Let (R, 𝔪) be a local ring, and let C be a semidualizing complex. We establish the equality r
R (Z)= ν (Ext⁡ R g− inf⁡ C (Z, C)) μ R depth⁡ C (𝔪, C) for a homologically finite and …