Diagonal tensor algebra and naive liftings
S Nasseh, M Ono, Y Yoshino - arXiv preprint arXiv:2309.05293, 2023 - arxiv.org
The notion of naive lifting of DG modules was introduced by the authors in [16, 17] for the
purpose of studying problems in homological commutative algebra that involve self …
purpose of studying problems in homological commutative algebra that involve self …
Triangulated Matlis equivalence
L Positselski - Journal of Algebra and Its Applications, 2018 - World Scientific
This paper is a sequel to [L. Positselski, Dedualizing complexes and MGM duality, J. Pure
Appl. Algebra 220 (12)(2016) 3866–3909, arXiv: 1503.05523 [math. CT]; Contraadjusted …
Appl. Algebra 220 (12)(2016) 3866–3909, arXiv: 1503.05523 [math. CT]; Contraadjusted …
[图书][B] Uniserial modules over commutative artin local rings
J Luo - 1994 - search.proquest.com
We study modules over a commutative artin local ring R. For the most part, we concentrate
on almost split sequences with uniserial modules in its end terms. Based on our …
on almost split sequences with uniserial modules in its end terms. Based on our …
[PDF][PDF] HOMOLOGICAL DIMENSIONS OF LOCAL (CO) HOMOLOGY OVER DERIVED COMMUTATIVE RINGS
L SHAUL - arXiv preprint arXiv:1702.01107, 2017 - researchgate.net
Let A be a commutative noetherian ring, let a⊆ A be an ideal, and let J be an injective A-
module. A basic result in the structure theory of injective modules states that the A-module …
module. A basic result in the structure theory of injective modules states that the A-module …
On modules with self Tor vanishing
O Celikbas, H Holm - Communications in Algebra, 2020 - Taylor & Francis
The long-standing Auslander and Reiten Conjecture states that a finitely generated module
over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors …
over a finite-dimensional algebra is projective if certain Ext-groups vanish. Several authors …
Relative Tor functors for level modules with respect to a semidualizing bimodule
J Hu, Y Geng - Algebras and Representation Theory, 2016 - Springer
Let R and S be rings and SCR a semidualizing bimodule. We investigate the relative Tor
functors Tor i ℳ ℒ C (−,−) Tor_i^ML_C(-,-) defined via C-level resolutions, and these functors …
functors Tor i ℳ ℒ C (−,−) Tor_i^ML_C(-,-) defined via C-level resolutions, and these functors …
Torsion-simple objects in abelian categories
S Pavon - arXiv preprint arXiv:2312.04384, 2023 - arxiv.org
We introduce the notion of torsion-simple objects in an abelian category: these are the
objects which are always either torsion or torsion-free with respect to any torsion pair. We …
objects which are always either torsion or torsion-free with respect to any torsion pair. We …
[HTML][HTML] Vanishing of Tor, and why we care about it
O Celikbas, R Wiegand - Journal of Pure and Applied Algebra, 2015 - Elsevier
Given finitely generated modules M and N over a local ring R, the tensor product M⊗ RN
typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free …
typically has nonzero torsion. Indeed, the assumption that the tensor product is torsion-free …
GENERALIZATIONS OF ARTINIAN AND NOETHERIAN MODULES
NH HWEE - 1995 - scholarbank.nus.edu.sg
This thesis is a study of generalizations of the dual concepts of an artinian module and a
noetherian module, called a semiartinian module and a seminoetherian module …
noetherian module, called a semiartinian module and a seminoetherian module …
Finite support of tensor products
M Asgharzadeh - arXiv preprint arXiv:1902.10509, 2019 - arxiv.org
We determine the submodule of finite support of the tensor product of two modules $ M $
and $ N $ over a local ring and estimate its length in terms of $ M $ and $ N $. Also, we …
and $ N $ over a local ring and estimate its length in terms of $ M $ and $ N $. Also, we …