[PDF][PDF] Studies on various conditions on Cohen–Macaulay rings and modules, with applications to the representation theory of maximal Cohen–Macaulay modules
T Kobayashi - (No Title), 2020 - nagoya.repo.nii.ac.jp
… By use of homological methods in commutative algebra, the notion of a Cohen-Macaulay …
In other words, M is generated by two elements as an R-module. Since M is nonfree, one has …
In other words, M is generated by two elements as an R-module. Since M is nonfree, one has …
On proper and exact relative homological dimensions
D Bennis, JR Garcia Rozas, L Mao… - Algebra Colloquium, 2020 - World Scientific
… -projective modules, where C is a semidualizing module. However… in the relative (co)homology
groups. The first main result of … relative (co)homology groups (see Theorems 5.3 and 5.5). …
groups. The first main result of … relative (co)homology groups (see Theorems 5.3 and 5.5). …
Generic constructions and semidualizing modules
SK Sather-Wagstaff, T Se, S Spiroff - Algebras and Representation Theory, 2021 - Springer
… , for investigation into homological properties of modules that, in … goal of describing all
semidualizing modules over certain classes … One aspect of our work in [21] is to localize our tensor …
semidualizing modules over certain classes … One aspect of our work in [21] is to localize our tensor …
Auslander-Reiten Conjecture, Finite -Injective Dimension of , and vanishing of
VD Mendoza-Rubio, VH Jorge-Pérez - arXiv preprint arXiv:2312.05914, 2023 - arxiv.org
… over a local ring is an actively researched topic in commutative algebra and homological …
provide criteria for a semidualizing module to be considered a canonical module of a Cohen-…
provide criteria for a semidualizing module to be considered a canonical module of a Cohen-…
[PDF][PDF] Relative Finitistic Projective and Injective Dimensions
Y Wei, X Tang - International Journal of Algebra, 2023 - m-hikari.com
… ] initiated the study of semidualizing modules over arbitrary associative rings. Semidualizing
modules have been a cornerstone of relative homological algebra. Several important results …
modules have been a cornerstone of relative homological algebra. Several important results …
GC-projectivity and injectivity under Frobenius extensions
Z Zhao - Communications in Algebra, 2022 - Taylor & Francis
… with respect to a semidualizing module are preserved under Frobenius … homological
dimensions are preserved under Frobenius extensions, which show that Gorenstein homological …
dimensions are preserved under Frobenius extensions, which show that Gorenstein homological …
Relative weak global Gorenstein dimension, AB-contexts and model structures
… a semidualizing (R, S)-bimodule C can be computed either by the GC -flat dimension of the
left R-modules or right S-modules… this subject from homological and homotopical aspects. We …
left R-modules or right S-modules… this subject from homological and homotopical aspects. We …
Some results on vanishing of Ext and finite Gorenstein dimension of the dual of a module
VD Mendoza-Rubio, VH Jorge-Pérez - arXiv preprint arXiv:2312.06124, 2023 - arxiv.org
… We recall that an R-module C is semidualizing if the natural map R → HomR(C, C) is an …
of the most celebrated problems in homological commutative algebra and states the following. …
of the most celebrated problems in homological commutative algebra and states the following. …
Balanced systems for
… From the notion of (co)generator in relative homological … by the finiteness of homological
dimensions relative to X and Y. … with a dualizing module D and a semidualizing module C. Other …
dimensions relative to X and Y. … with a dualizing module D and a semidualizing module C. Other …
[PDF][PDF] EXTENSION CLOSURE OF ADJOINT COTORSIONFREE MODULES
XI TANG, Z HUANG - maths.nju.edu.cn
… modules with respect to a semidualizing bimodule RωS by using the properties of the (strong)
grade of modules. In [… of n-ω-cotorsionfree modules and adjoint n-ω-cotorsionfree modules …
grade of modules. In [… of n-ω-cotorsionfree modules and adjoint n-ω-cotorsionfree modules …