Trace ideal and annihilator of Ext and Tor of regular fractional ideals, and some applications
S Dey - arXiv preprint arXiv:2210.03891, 2022 - arxiv.org
Given a commutative Noetherian ring $ R $ with total ring of fractions $ Q (R) $, and a finitely
generated $ R $-submodule $ M $ of $ Q (R) $, we prove an equality between trace ideal …
generated $ R $-submodule $ M $ of $ Q (R) $, we prove an equality between trace ideal …
A generalization of the dimension and radius of a subcategory of modules and its applications
Y Mifune - arXiv preprint arXiv:2401.11153, 2024 - arxiv.org
Let $ R $ be a commutative noetherian local ring and denote by $\operatorname {mod} R $
the category of finitely generated $ R $-modules. In this paper, we give some evaluations of …
the category of finitely generated $ R $-modules. In this paper, we give some evaluations of …
Compactness of the Alexandrov topology of maximal Cohen-Macaulay modules
K Kimura - arXiv preprint arXiv:2401.04987, 2024 - arxiv.org
Let $ R $ be a Cohen-Macaulay local ring. In this paper, we first describe the radicals of
annihilators of stable categories of maximal Cohen-Macaulay $ R $-modules. We then prove …
annihilators of stable categories of maximal Cohen-Macaulay $ R $-modules. We then prove …
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 …