Journal ArticleDOI
Coherent rings with finite self-FP-injective dimension
Nanqing Ding,Jianlong Chen +1 more
TLDR
In this paper, the authors generalize the characterization of Gorenstein flat modules over GNNs to n − FC rings (coherent rings with finite sdf−FP−injective dimension).Abstract:
In this paper, we generalize the characterization of Gorenstein flat modules over Gorenstein rings to n − FC rings (coherent rings with finite sdf−FP−injective dimension), and characterize n − FC rings in terms of Gorenstein flat and projective modules.read more
Citations
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Journal ArticleDOI
Model structures on modules over Ding-Chen rings
TL;DR: In this paper, Ding projective, Ding injective and Ding flat modules are defined as analogs to Enochs' Gorenstein projective and Gorentein flat modules.
Journal ArticleDOI
Strongly gorenstein flat modules
TL;DR: In this article, strongly Gorenstein flat R-modules are introduced and investigated, and the existence of strongly flat precovers and pre-envelopes is shown. But the strongly Gorestein flat dimension is not investigated.
Journal ArticleDOI
Gorenstein fp-injective and gorenstein flat modules
Lixin Mao,Nanqing Ding +1 more
TL;DR: Gorenstein FP-injective R-modules over coherent rings were studied in this article, where several known results were extended and some properties of Gorenstein flat modules were obtained.
Journal ArticleDOI
Rings Over Which the Class of Gorenstein Flat Modules is Closed Under Extensions
TL;DR: In this article, the authors investigated the dimension of left GF-closed rings and showed how to construct a left GF closed ring that is neither right coherent nor of finite weak dimension.
Posted Content
Rings over which the class of Gorenstein flat modules is closed under extensions
TL;DR: In this article, the authors investigated the dimension of left GF-closed rings and showed how to construct a left GF closed ring that is neither right coherent nor of finite weak dimension.
References
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Book
An Introduction to Homological Algebra
TL;DR: An Introduction to Homological Algebra as discussed by the authors discusses the origins of algebraic topology and presents the study of homological algebra as a two-stage affair: first, one must learn the language of Ext and Tor and what it describes.
Journal ArticleDOI
On the ubiquity of Gorenstein rings
TL;DR: Recently, the authors showed that if W is a subvariety of codimension q at all of its points, then W is non-singular, and W is defined, and GROTHENDIECK has shown that W = 2 d o if, and only if, f2b is a free 9 of rank one.
Book
Commutative Coherent Rings
TL;DR: In this paper, the authors introduce the notion of coherent rings and coherent algebras as fundamental concepts for ring extensions and constructions and overrings, as well as particular coherent rings.