On Gorenstein projective, injective and flat dimensions-a functorial description with applications

LW Christensen, A Frankild, H Holm - arXiv preprint math/0403156, 2004 - arxiv.org
Gorenstein homological dimensions are refinements of the classical homological
dimensions, and finiteness singles out modules with amenable properties reflecting those of …

[PDF][PDF] Some characterizations of Gorenstein local rings in terms of G-dimension

R Takahashi - Acta Mathematica Hungarica, 2004 - math.nagoya-u.ac.jp
SOME CHARACTERIZATIONS OF GORENSTEIN LOCAL RINGS IN TERMS OF G-DIMENSION
1. Introduction and Preliminary Throughout the present Page 1 SOME CHARACTERIZATIONS …

Commutative extensions by canonical modules are Gorenstein rings

R Fossum - Proceedings of the American Mathematical Society, 1973 - ams.org
Reiten has demonstrated that the trivial Hochschild extension of a Cohen-Macaulay local
ring by a canonical module is a Gorenstein local ring. Here it is proved that any commutative …

Stability of Gorenstein categories

KA Sather-Wagstaff, T Sharif… - Journal of the London …, 2008 - Wiley Online Library
We show that an iteration of the procedure used to define the Gorenstein projective modules
over a commutative ring R yields exactly the Gorenstein projective modules. Specifically …

Strongly Gorenstein projective, injective and flat modules

X Yang, Z Liu - Journal of Algebra, 2008 - Elsevier
Journal of Algebra Strongly Gorenstein projective, injective and flat modules Page 1 Journal
of Algebra 320 (2008) 2659–2674 Contents lists available at ScienceDirect Journal of Algebra …

The derived category of a graded Gorenstein ring

J Burke, G Stevenson - Commutative algebra and …, 2013 - books.google.com
We give an exposition and generalization of Orlov's theorem on graded Gorenstein rings.
We show the theorem holds for nonnegatively graded rings that are Gorenstein in an …

Gorenstein flat covers over GF-closed rings

Y Gang, L Zhongkui - Communications in Algebra, 2012 - Taylor & Francis
Full article: Gorenstein Flat Covers over GF-Closed Rings Skip to Main Content Taylor and
Francis Online homepage Taylor and Francis Online homepage Log in | Register Cart 1.Home …

Projectively coresolved Gorenstein flat and ding projective modules

A Iacob - Communications in Algebra, 2020 - Taylor & Francis
We give necessary and sufficient conditions in order for the class of projectively coresolved
Gorenstein flat modules, PGF (respectively that of projectively coresolved Gorenstein B flat …

On stability of Gorenstein categories

A Xu, N Ding - Communications in Algebra, 2013 - Taylor & Francis
We show that an iteration of the procedure used to define the Gorenstein projective modules
over a ring R yields exactly the Gorenstein projective modules. Specifically, given an exact …

Injective modules for group rings and Gorenstein orders

KW Roggenkamp - Journal of Algebra, 1973 - Elsevier
Commutative noetherian Gorenstein rings (ie, rings of finite selfinjective dimension) were
first studied by Bass in 1963 [2]. S is a Gorenstein ring of injective dimension one if and only …