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 …
Auslander-Reiten conjecture in a dual vein
H Eshraghi, A Mahin Fallah - Algebras and Representation Theory, 2021 - Springer
We consider a dual notion of the famous Auslander-Reiten Conjecture in case of Noetherian
algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its …
algebras over commutative Noetherian rings. Firstly, in the introduction, we will examine its …
Torsion functors, small or large
F Rohrer - Beiträge zur Algebra und Geometrie/Contributions to …, 2019 - Springer
Let aa be an ideal in a commutative ring R. For an R-module M, we consider the small a a-
torsion Γ _ a (M)={x ∈ M ∣ ∃ n ∈ N: a^ n ⊆ (0: _Rx)\} Γ a (M)= x∈ M∣∃ n∈ N: an⊆(0: R …
torsion Γ _ a (M)={x ∈ M ∣ ∃ n ∈ N: a^ n ⊆ (0: _Rx)\} Γ a (M)= x∈ M∣∃ n∈ N: an⊆(0: R …
Homological Properties of Structures in Commutative Algebra and Algebraic Combinatorics
JL Lyle - 2020 - search.proquest.com
The purpose of this work is to understand homological properties of structures appearing in
commutative algebra and algebraic combinatorics, objects such as commutative rings and …
commutative algebra and algebraic combinatorics, objects such as commutative rings and …
[PDF][PDF] Cartan-Eilenberg complexes and Foxby equivalence
R Wei, L Bo, Z Chunxia, L Zhongkui - arXiv preprint arXiv:1408.6728, 2014 - Citeseer
The main aim of this paper is to investigate Cartan-Eilenberg complexes with respect to a
semidualizing module, and extend the existed Foxby equivalence. To this end, we define …
semidualizing module, and extend the existed Foxby equivalence. To this end, we define …
Criteria for flatness and injectivity
N Epstein, Y Yao - Mathematische Zeitschrift, 2012 - Springer
Let R be a commutative Noetherian ring. We give criteria for flatness of R-modules in terms
of associated primes and torsion-freeness of certain tensor products. This allows us to …
of associated primes and torsion-freeness of certain tensor products. This allows us to …
Vanishing of relative homology and depth of tensor products
O Celikbas, L Liang, A Sadeghi - Journal of Algebra, 2017 - Elsevier
For finitely generated modules M and N over a Gorenstein local ring R, one has depth M+
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …
depth N= depth (M⊗ RN)+ depth R, ie, the depth formula holds, if M and N are Tor …
[PDF][PDF] An introduction to Auslander-Reiten theory
LA Hügel - Lecture notes, ICTP Trieste, 2006 - profs.scienze.univr.it
We will only assume some basic knowledge in module theory and category theory. In
particular, we will use the following notions that can be found in any textbook on modules or …
particular, we will use the following notions that can be found in any textbook on modules or …
T-structures of Happel-Reiten-Smal∅ whose hearts are module categories
C Parra, M Saorín - profs.sci.univr.it
Given an associative ring R and a torsion pair t=(T, F) in the category of left R-modules, the
heart Ht of the t-structure associated to t, is an abelian category (see [BBD]). In [HKM], the …
heart Ht of the t-structure associated to t, is an abelian category (see [BBD]). In [HKM], the …