Auslander-Reiten conjecture for modules whose (self) dual has finite complete intersection dimension
D Ghosh, M Samanta - arXiv preprint arXiv:2405.01497, 2024 - arxiv.org
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 …
for the class of (finitely generated) modules whose dual has finite complete intersection …
Auslander--Reiten conjecture for normal rings
K Kimura - arXiv preprint arXiv:2304.03956, 2023 - arxiv.org
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 …
noetherian ring to be projective are given in terms of vanishing of Ext modules. One of the …
Vanishing of Tor over fiber products
T Freitas, V Pérez, R Wiegand, S Wiegand - Proceedings of the American …, 2021 - ams.org
Let $(S,\mathfrak {m}, k) $ and $(T,\mathfrak {n}, k) $ be local rings, and let $ R $ denote their
fiber product over their common residue field $ k $. Inspired by work of Nasseh and Sather …
fiber product over their common residue field $ k $. Inspired by work of Nasseh and Sather …
Trace ideals of canonical modules, annihilators of Ext modules, and classes of rings close to being Gorenstein
In this note we study trace ideals of canonical modules. Characterizations of the trace ideals
in terms of annihilators of certain Ext modules are given. We apply our results to study many …
in terms of annihilators of certain Ext modules are given. We apply our results to study many …
On Gorenstein fiber products and applications
We show that a non-trivial fiber product $ S\times_k T $ of commutative noetherian local
rings $ S, T $ with a common residue field $ k $ is Gorenstein if and only if it is a …
rings $ S, T $ with a common residue field $ k $ is Gorenstein if and only if it is a …
On General fiber product rings, Poincar\'e series and their structure
TH Freitas, JA Lima - arXiv preprint arXiv:2402.12125, 2024 - arxiv.org
The present paper deals with the investigation of the structure of general fiber product rings
$ R\times_TS $, where $ R $, $ S $ and $ T $ are local rings with common residue field. We …
$ R\times_TS $, where $ R $, $ S $ and $ T $ are local rings with common residue field. We …
Self-injective commutative rings have no nontrivial rigid ideals
H Lindo - arXiv preprint arXiv:1710.01793, 2017 - arxiv.org
arXiv:1710.01793v2 [math.AC] 13 Oct 2017 Page 1 arXiv:1710.01793v2 [math.AC] 13 Oct
2017 SELF-INJECTIVE COMMUTATIVE RINGS HAVE NO NONTRIVIAL RIGID IDEALS …
2017 SELF-INJECTIVE COMMUTATIVE RINGS HAVE NO NONTRIVIAL RIGID IDEALS …
Some Categorical Aspects of Commutative Algebra
S Dey - 2023 - search.proquest.com
The purpose of this work is to study commutative Noetherian rings by studying certain
subcategories of the category of finitely generated modules over such rings. We begin by …
subcategories of the category of finitely generated modules over such rings. We begin by …
On the nonrigidity of trace modules
H Lindo - Journal of Commutative Algebra, 2022 - projecteuclid.org
We establish a link between trace modules and rigidity in modules over Noetherian rings.
We identify classes of modules which must have self-extensions and use the theory of trace …
We identify classes of modules which must have self-extensions and use the theory of trace …
[PDF][PDF] VANISHING OF EXT MODULES OVER COHEN–MACAULAY RINGS
VANISHING OF EXT MODULES OVER COHEN–MACAULAY RINGS 1. Introduction We refer
the reader to [10] (arXiv:2106.08583) for details Page 1 VANISHING OF EXT MODULES OVER …
the reader to [10] (arXiv:2106.08583) for details Page 1 VANISHING OF EXT MODULES OVER …