The balance of relative Ext groups defined by semidualizing modules
KA Beigi, K Divaani-Aazar, M Tousi - Journal of Algebra and Its …, 2023 - World Scientific
Let R be a commutative Noetherian ring with identity and C a semidualizing module for R.
Let 𝒫 C (R) and ℐ C (R) denote, respectively, the classes of C-projective and C-injective R …
Let 𝒫 C (R) and ℐ C (R) denote, respectively, the classes of C-projective and C-injective R …
The balance of relative Ext groups defined by semi dualizing modules
K Abolfath Beigi, K Divaani-Aazar, M Tousi - arXiv e-prints, 2022 - ui.adsabs.harvard.edu
Let $ R $ be a commutative Noetherian ring with identity and $ C $ a semidualizing module
for $ R $. Let $\mathscr {P} _C (R) $ and $\mathscr {I} _C (R) $ denote, respectively, the …
for $ R $. Let $\mathscr {P} _C (R) $ and $\mathscr {I} _C (R) $ denote, respectively, the …
Torsor-cotorsor duality of Ext groups
N Mertes - arXiv preprint arXiv:2006.15996, 2020 - arxiv.org
Let $ A $ be a ring, and let $ M $ and $ N $ be $ A $-modules. Then $ N $ can be viewed as
a group object in the category $ A $-Mod/$ M $ of $ A $-modules over $ M $ and Ext $^ 1 (M …
a group object in the category $ A $-Mod/$ M $ of $ A $-modules over $ M $ and Ext $^ 1 (M …
A characterization of Auslander category
J Sun - Turkish Journal of Mathematics, 2013 - journals.tubitak.gov.tr
In this paper, we discuss the Bass class and the Auslander class with respect to a
semidualizing module over an associative ring. Let _SC_R be a semidualizing module, we …
semidualizing module over an associative ring. Let _SC_R be a semidualizing module, we …
Cotorsion theories involving Auslander and Bass classes
Z Zhang, X Zhu, X Yan - Communications in Algebra, 2012 - Taylor & Francis
Let R be a commutative ring, 𝒞 be a semidualizing R-module. We show that the Auslander
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …
class 𝒜𝒞 (R) with respect to 𝒞 is the first left orthogonal class of some pure injective module …
Relative Tor functors with respect to a semidualizing module
Let C be a semidualizing module over a commutative noetherian ring R. We exhibit an
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
isomorphism Tor^F_CM_i(-,-)≅Tor^P_CM_i(-,-) between the bifunctors defined via C-flat and …
Cograde conditions and cotorsion pairs
X Tang, Z Huang - Publications of the Research Institute for …, 2020 - ems.press
Let R and S be rings and RωS a semidualizing bimodule. We investigate when the double
functor TorS i (ω, Exti R (ω,−)) preserves epimorphisms and the double functor Exti R (ω …
functor TorS i (ω, Exti R (ω,−)) preserves epimorphisms and the double functor Exti R (ω …
Cotorsion dimensions relative to semidualizing modules
X Chen, J Chen - Journal of Algebra and Its Applications, 2016 - World Scientific
Let C be a semidualizing R-module, where R is a commutative ring. We first introduce the
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …
definition of C-cotorsion modules, and obtain the properties of C-cotorsion modules. As …
Tensor and torsion products of relative injective modules with respect to a semidualizing module
Let R be a commutative Cohen–Macaulay ring, and let C be a semidualizing module of R. In
this paper, we show that C is generically dualizing if and only if the tensor products of …
this paper, we show that C is generically dualizing if and only if the tensor products of …
Tensor Product of -Injective Modules
M Rahmani, AJ Taherizadeh - arXiv preprint arXiv:1503.05492, 2015 - arxiv.org
Let $ R $ be a Noetherian ring and let $ C $ be a semidualizing $ R $-module. In this paper,
we are concerned with the tensor and torsion product of $ C $-injective modules. Firstly, it is …
we are concerned with the tensor and torsion product of $ C $-injective modules. Firstly, it is …