FP-injectivity relative to a semidualizing bimodule

2012 ◽  
Vol 80 (3-4) ◽  
pp. 311-326 ◽  
Author(s):  
XI TANG
Keyword(s):  
Semidualizing Bimodule

Homological Behavior of Relative Cotorsionfree and Cosyzygy Modules

2019 ◽  
Vol 26 (03) ◽  
pp. 467-478
Author(s):  
Guoqiang Zhao ◽  
Bo Zhang
Keyword(s):  
Torsionfree Module ◽  
Semidualizing Bimodule

As the dual of the Auslander transpose and the resulting k-torsionfree module, the cotranspose and k-cotorsionfree module with respect to a semidualizing bimodule have been introduced recently. In this paper we first investigate the relation between relative k-cotorsionfree modules and relative k-cosyzygy modules. Then we study the extension closure of these two classes of modules.

scholarly journals Totally reflexive modules with respect to a semidualizing bimodule

2013 ◽  
Vol 63 (2) ◽  
pp. 385-402 ◽  
Author(s):  
Zhen Zhang ◽  
Xiaosheng Zhu ◽  
Xiaoguang Yan
Keyword(s):  
Semidualizing Bimodule ◽  
Reflexive Modules

WEAK AB-CONTEXT FOR FP-INJECTIVE MODULES WITH RESPECT TO SEMIDUALIZING MODULES

2013 ◽  
Vol 12 (07) ◽  
pp. 1350039 ◽  
Author(s):  
JIANGSHENG HU ◽  
DONGDONG ZHANG
Keyword(s):  
Noetherian Ring ◽  
Model Structure ◽  
Injective Dimension ◽  
Commutative Noetherian Ring ◽  
New Model ◽  
Injective Modules ◽  
Semidualizing Modules ◽  
Semidualizing Bimodule ◽  
Gorenstein Injective

Let S and R be rings and SCR a semidualizing bimodule. We define and study GC-FP-injective R-modules, and these modules are exactly C-Gorenstein injective R-modules defined by Holm and Jørgensen provided that S = R is a commutative Noetherian ring. We mainly prove that the category of GC-FP-injective R-modules is a part of a weak AB-context, which is dual of weak AB-context in the terminology of Hashimoto. In particular, this allows us to deduce the existence of certain Auslander–Buchweitz approximations for R-modules with finite GC-FP-injective dimension. As an application, a new model structure in Mod R is given.

Semidualizing bimodules and related Gorenstein homological dimensions

2016 ◽  
Vol 15 (10) ◽  
pp. 1650193 ◽  
Author(s):  
Aimin Xu ◽  
Nanqing Ding
Keyword(s):  
Projective Dimension ◽  
Negative Integer ◽  
Homological Dimensions ◽  
Semidualizing Bimodule ◽  
Finitely Presented

Let [Formula: see text] be a semidualizing bimodule with [Formula: see text] left coherent and [Formula: see text] right coherent. For a non-negative integer [Formula: see text], it is shown that [Formula: see text]-[Formula: see text]-[Formula: see text] if and only if every finitely presented left [Formula: see text]-module has [Formula: see text]-projective dimension at most [Formula: see text] if and only if every finitely presented right [Formula: see text]-module has [Formula: see text]-projective dimension at most [Formula: see text]. As applications, some well-known results are extended.

SEMIDUALIZING MODULES AND RELATED MODULES

2011 ◽  
Vol 10 (06) ◽  
pp. 1261-1282 ◽  
Author(s):  
DONGDONG ZHANG ◽  
BAIYU OUYANG
Keyword(s):  
Noetherian Ring ◽  
Injective Modules ◽  
Bass Class ◽  
Derived Functors ◽  
Semidualizing Modules ◽  
Left And Right ◽  
Definition Of ◽  
Semidualizing Bimodule ◽  
Coherent Rings

In this paper, we prove that the Bass class [Formula: see text] with respect to a semidualizing bimodule C contains all FP-injective S-modules. We introduce the definition of C-FP-injective modules, and give some characterizations of right coherent rings in terms of the C-flat S-modules and C-FP-injective S op -modules. We discuss when every S-module has an C-flat preenvelope which is epic (or monic). In addition, we investigate the left and right [Formula: see text]-resolutions of R-modules by left derived functors Ext n(-, -) over a left Noetherian ring S. As applications, some new characterizations of left perfect rings are induced by these modules associated with C. A few classical results of these rings are obtained as corollaries.

scholarly journals Ding projective modules with respect to a semidualizing bimodule

2015 ◽  
Vol 45 (4) ◽  
pp. 1389-1411 ◽  
Author(s):  
Chunxia Zhang ◽  
Limin Wang ◽  
Zhongkui Liu
Keyword(s):  
Projective Modules ◽  
Semidualizing Bimodule

scholarly journals Duality pairs induced by Auslander and Bass classes

2021 ◽  
Vol 0 (0) ◽  
Author(s):  
Zhaoyong Huang
Keyword(s):  
Projective Dimension ◽  
Duality Pairs ◽  
Semidualizing Bimodule

Abstract Let R and S be arbitrary rings and let C S R {{}_{R}C_{S}} be a semidualizing bimodule, and let 𝒜 C ⁢ ( R op ) {\mathcal{A}_{C}(R^{\mathrm{op}})} and ℬ C ⁢ ( R ) {\mathcal{B}_{C}(R)} be the Auslander and Bass classes, respectively. Then both pairs ( 𝒜 C ⁢ ( R op ) , ℬ C ⁢ ( R ) )   and   ( ℬ C ⁢ ( R ) , 𝒜 C ⁢ ( R op ) ) (\mathcal{A}_{C}(R^{\mathrm{op}}),\mathcal{B}_{C}(R))\quad\text{and}\quad(% \mathcal{B}_{C}(R),\mathcal{A}_{C}(R^{\mathrm{op}})) are coproduct-closed and product-closed duality pairs and both 𝒜 C ⁢ ( R op ) {\mathcal{A}_{C}(R^{\mathrm{op}})} and ℬ C ⁢ ( R ) {\mathcal{B}_{C}(R)} are covering and preenveloping; in particular, the former duality pair is perfect. Moreover, if ℬ C ⁢ ( R ) {\mathcal{B}_{C}(R)} is enveloping in Mod ⁡ R {\operatorname{Mod}R} , then 𝒜 C ⁢ ( S ) {\mathcal{A}_{C}(S)} is enveloping in Mod ⁡ S {\operatorname{Mod}S} . Also, some applications to the Auslander projective dimension of modules are given.

Gorenstein Projective Dimension Relative to a Semidualizing Bimodule

2013 ◽  
Vol 41 (1) ◽  
pp. 1-18 ◽  
Author(s):  
Zengfeng Liu ◽  
Zhaoyong Huang ◽  
Aimin Xu
Keyword(s):  
Projective Dimension ◽  
Semidualizing Bimodule
Sign in / Sign up

Export Citation Format

Share Document