On relative counterpart of Auslander's conditions
It is now well known that the conditions used by Auslander to define the Gorenstein
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …
projective modules on Noetherian rings are independent. Recently, Ringel and Zhang …
On Auslander-type conditions of modules
Z Huang - arXiv preprint arXiv:1012.1703, 2010 - arxiv.org
We prove that for a left and right Noetherian ring $ R $, $ _RR $ satisfies the Auslander
condition if and only if so does every flat left $ R $-module, if and only if the injective …
condition if and only if so does every flat left $ R $-module, if and only if the injective …
Gorenstein injective modules and Auslander categories
MA Esmkhani, M Tousi - Archiv der Mathematik, 2007 - Springer
In this paper, we study Gorenstein injective modules over a local Noetherian ring R. For an
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …
R-module M, we show that M is Gorenstein injective if and only if Hom R (Ȓ, M) belongs to …
New characterizations of dualizing modules
X Tang - Communications in Algebra, 2012 - Taylor & Francis
Let R be a commutative Noetherian ring. In this article, we provide some new criteria for a
semidualizing module to be dualizing in terms of special homological properties of module …
semidualizing module to be dualizing in terms of special homological properties of module …
Buchweitz's equivalences for Gorenstein flat modules with respect to semidualizing modules
J Hu, Y Geng, J Wu, H Li - Journal of Algebra and Its Applications, 2021 - World Scientific
Let R be a commutative Noetherian ring and C a semidualizing R-module. We obtain an
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …
exact structure (ℋ C, 𝜀) and prove that the full subcategory ℋ C∩ 𝒢 ℱ C of ℋ C is a …
A generalization of strongly Gorenstein projective modules
D Bennis, N Mahdou - Journal of Algebra and its Applications, 2009 - World Scientific
This paper generalize the idea of the authors in J. Pure Appl. Algebra 210 (2007) 437–445.
Namely, we define and study a particular case of Gorenstein projective modules. We …
Namely, we define and study a particular case of Gorenstein projective modules. We …
[PDF][PDF] The Bongartz's theorem of Gorenstein cosilting complexes
H Yao, Q Yuan - 대한수학회지, 2023 - koreascience.kr
We describe the Gorenstein derived categories of Gorenstein rings via the homotopy
categories of Gorenstein injective modules. We also introduce the concept of Gorenstein …
categories of Gorenstein injective modules. We also introduce the concept of Gorenstein …
(X, Y)-Gorenstein projective and injective modules
Q Pan, F Cai - Turkish Journal of Mathematics, 2015 - journals.tubitak.gov.tr
This paper introduces and studies (X, Y)-Gorenstein projective and injective modules, which
are a generalization of Enochs' Gorenstein projective and injective modules, respectively …
are a generalization of Enochs' Gorenstein projective and injective modules, respectively …
Foxby equivalences associated to strongly Gorenstein modules
W Zhang, Z Liu, X Yang - Kodai Mathematical Journal, 2018 - jstage.jst.go.jp
In order to establish the Foxby equivalences associated to strongly Gorenstein modules, we
introduce the notions of strongly WP-Gorenstein, WI-Gorenstein and WF-Gorenstein …
introduce the notions of strongly WP-Gorenstein, WI-Gorenstein and WF-Gorenstein …
[PDF][PDF] Applications of n-Gorenstein projective and injective modules
X Tang - Hacettepe Journal of Mathematics and Statistics, 2015 - dergipark.org.tr
Over a commutative noetherian ring, we introduce a generalization of Gorenstein projective
and injective modules, which we call, respectively, n-Gorenstein projective and injective …
and injective modules, which we call, respectively, n-Gorenstein projective and injective …