Gorenstein weak injective modules with respect to a semidualizing bimodule

Z Gao, X Ma, T Zhao - Journal of the Korean Mathematical Society, 2018 - koreascience.kr
In this paper, we introduce the notion of C-Gorenstein weak injective modules with respect to
a semidualizing bimodule $ _SC_R $, where R and S are arbitrary associative rings. We …

[PDF][PDF] Gorenstein homological properties from coherent rings to arbitary rings

TW Zhao, YG Xu - arXiv preprint arXiv:1405.3375, 2014 - Citeseer
Throughout R is an associative ring with identity and all modules are unitary. Unless stated
otherwise, an R-module will be understood to be a left R-module. As usual, pdR (M) and idR …

Generalized Gorenstein modules

A Iacob - Algebra Colloquium, 2022 - World Scientific
We introduce a generalization of the Gorenstein injective modules: the Gorenstein FP n-
injective modules (denoted by GI n). They are the cycles of the exact complexes of injective …

[HTML][HTML] Homotopy category of projective complexes and complexes of Gorenstein projective modules

J Asadollahi, R Hafezi, S Salarian - Journal of Algebra, 2014 - Elsevier
Let R be a ring with identity and C (R) denote the category of complexes of R-modules. In
this paper we study the homotopy categories arising from projective (resp. injective) …

Gorenstein injective and projective complexes

EE Enochs, JR Garcí Rozas - Communications in Algebra, 1998 - Taylor & Francis
In this article we extend the notion of Gorenstein injective and projective modules to that of
complexes and characterize such complexes. We prove that over an n-Gorenstein ring every …

n-Strongly Gorenstein Projective, Injective and Flat Modules

G Zhao, Z Huang - Communications in Algebra, 2011 - Taylor & Francis
In this article, we study the relation between m-strongly Gorenstein projective (resp.,
injective) modules and n-strongly Gorenstein projective (resp., injective) modules whenever …

[PDF][PDF] Rings over which all modules are gorenstein (resp., strongly gorenstein) projective

D Bennis, N Mahdou, K Ouarghi - arXiv preprint arXiv:0712.0127, 2007 - Citeseer
One of the main results of this paper is the characterization of the rings over which all
modules are strongly Gorenstein projective. We show that these kinds of rings are very …

Gorenstein projective modules and Frobenius extensions

W Ren - Science China Mathematics, 2018 - Springer
We prove that for a Frobenius extension, if a module over the extension ring is Gorenstein
projective, then its underlying module over the base ring is Gorenstein projective; the …

Gorenstein injective and projective complexes with respect to a semidualizing module

C Yang, L Liang - Communications in Algebra, 2012 - Taylor & Francis
Let R be a commutative (possibly non-Noetherian) ring (in order to make things less
technical) and C a semidualizing R-module. In this article, we introduce and investigate the …

On Gorenstein injective and projective comodules

QX Pan, Q Li - Mathematical Notes, 2013 - Springer
Gorenstein injective, projective and coflat comodules were introduced and studied by
Asensio and Enochs et al. We further investigate these comodules and introduce n …