3 citations · 11 across the 36 of their papers we have counts for
15 papers · 1 filter
Semi-regular flat modules over strong Prüfer rings
Xiaolei Zhang, Guocheng Dai, Xuelian Xiao +1
We first introduce and study the notion of semi-regular flat modules, and then show that a ring is a strong \Prufer\ ring if and only if every submodule of a semi-regular flat…
On -flatness and -coherence
Xiaolei Zhang, Wei Qi
In this paper, we introduce and study the notions of -flat modules and -coheret rings. First, by investigating the Nagata rings of -torsion theory, we show that the…
A homological characterization of -Prüfer -multiplication rings
Xiaolei Zhang
Let be a commutative ring. An -module is called a semi-regular -flat module if $\Tor_1^R(R/I,M)$ is $\GV$-torsion for any finitely generated semi-regular ideal . I…
On uniformly -absolutely pure modules
Xiaolei Zhang
Let be a commutative ring with identity and a multiplicative subset of . In this paper, we introduce and study the notions of -pure -exact sequences and -absolu…
A note on -Prüfer -multiplication rings
Xiaolei Zhang
In this note, we show that a strongly -ring is a -PvMR if and only if any -torsion free -module is --flat, if and only if any divisible module is nonnil-absol…
The -global dimensions of commutative rings
Xiaolei Zhang, Wei Qi
Let be a commutative ring with identity and a multiplicative subset of . First, we introduce and study the -projective dimensions and -injective dimensions of -…
On --Flat modules and Their Homological Dimensions
Xiaolei Zhang, Wei Zhao
In this paper, we introduce and study the class of --flat modules which are generalizations of both -flat modules and -flat modules. The --weak global dimension $…
The Telescope Conjecture for von Neumann regular rings
Xiaolei Zhang
In this note, we show that any epimorphism originating at a von Neumann regular ring (not necessary commutative) is a universal localization. As an application, we prove that the T…
Characterizing -projective modules and -semisimple rings by uniformity
Xiaolei Zhang, Wei Qi
Let be a ring and a multiplicative subset of . An -module is called uniformly -projective provided that the induced sequence $0\rightarrow \mathrm{Hom}_R(P,A)\…
The -weak global dimension of commutative rings
Xiaolei Zhang
In this paper, we introduce and study the -weak global dimension -w.gl.dim of a commutative ring for some multiplicative subset of . Moreover, commutative rin…
Characterizing -flat modules and -von Neumann regular rings by uniformity
Xiaolei Zhang
Let be a ring and a multiplicative subset of . An -module is called --torsion (- always abbreviates uniformly) provided that for some . Th…
Some remarks on nonnil-coherent rings and -IF rings
Wei Qi, Xiaolei Zhang
Let be a commutative ring. If the nilpotent radical of is a divided prime ideal, then is called a -ring. In this paper, we first distinguish the classes of…
New Characterizations of -coherent rings
Wei Qi, Xiaolei Zhang, Wei Zhao
In this paper, we introduce and study the class --ML of -Mittag-Leffler modules with respect to all flat modules. We show that a ring is -coherent if and…
The small finitistic dimensions of commutative rings
Xiaolei Zhang, Fanggui Wang
Let be a commutative ring with identity. The small finitistic dimension $\fPD(R)$ of is defined to be the supremum of projective dimensions of -modules with finite proje…
Some Remarks on -Dedekind rings and -Prufer rings
Xiaolei Zhang, Wei Qi
In this paper, the notions of nonnil-injective modules and nonnil-FP-injective modules are introduced and studied. Especially, we show that a -ring is an integral domain if…