2 citations · 6 across the 26 of their papers we have counts for
28 papers
On the -Weak Global Dimensions and -Global Dimensions
Xiaolei Zhang, Wei Qi
Let be a -ring and put . We determine the -weak global dimension of every -Prüfer ring. Its only possible values are , , and : the value is …
On the n-perfectness under split nilpotent extensions
Wei Qi, Xiaolei Zhang
Let be a split ring epimorphism with nilpotent kernel , and let be a fixed ring-theoretic section. We prove a change-of-rings form…
On the iso-Artinianness of one-dimensional Noetherian rings
Xiaolei Zhang, Ran Yan, Wei Qi
Let be a one-dimensional commutative Noetherian ring with a unique minimal prime such that is a principal ideal domain. We give a complete chara…
Transpose Symmetry of Injectivity over Commutative Semirings
Sixuan Gu, Wei Qi, Yaoyu Cheng
Let R be a commutative semiring, not necessarily with a multiplicative identity, and let A be an element of Mn(R). We prove that the map x to Ax on Rn is injective if and only if x…
A Generalized Supercongruence of Z.-W. Sun
Wei-Wei Qi
In this paper, we employ the Wilf-Zeilberger (WZ) method to prove a supercongruence conjecture posed by Z.-W. Sun: for any prime , \begin{align*} \sum_{k=0}^{\frac{p-3}{2}}\frac…
A survey on the uniform -version of rings, modules and their homological theories
Xiaolei Zhang, Wei Qi
This survey provides a comprehensive overview of the recent advancements in the theory of ``uniformly ''-algebraic structures in commutative ring theory. Originating from the cl…
Further q-Supercongruences from Singh's Quadratic Transformation
Wei-Wei Qi
In this paper, we investigate some q-congruences for truncated series by using Singh's quadratic transformation and the creative microscoping method (introduced by Vict…
Some Congruences Involving Binomial Coefficient and Fermat Quotient
Wei-Wei Qi
In this paper, we investigate some congruences involving sums of , where be a -adic integer, be a non-negative int…
Some remarks on --Noetherian and --coherent rings
Xiaolei Zhang, Wei Qi
In this paper, we give some new characterizations of --Noetherian rings and --coherent rings in terms of uniform -version of injective precovers, flat preenvelopes a…
A note on pure-semisimple rings
Xiaolei Zhang, Wei Qi
In this note, we give several characterizations of left pure-semisimple in terms of the (pre)envelope, (pre)cover, direct limits, direct sums, inverse limits and direct products pr…
A new version of P-flat modules and its applications
Wei Qi, Xiaolei Zhang
In this paper, we introduce and study the class of --P-flat modules, which can be seen as generalizations of both -P-flat modules and -P-flat modules. In particular, we…
Two remarks on Almost Projective Modules
Xiaolei Zhang, Wei Qi, Dechuan Zhou
For a commutative ring , an almost projective module is a module whose localization at every maximal ideal is free, with no restriction on rank. We prove that every almost proje…
On -weak global dimensions of commuative rings
Xiaolei Zhang, Ning Bian, Refat Abdelmawla Khaled Assaad +1
In this paper, the -weak global dimension -\cwd of a commutative ring is introduced. Rings with -weak global dimension equal to are studied in terms of…
Two new -supercongruences arising from Carlitz's identity
Ji-Cai Liu, Wei-Wei Qi
From Carlitz's identity, we deduce two new -supercongruences modulo the square of a cyclotomic polynomial, which were originally conjectured by Guo. These results establish new…
On strongly --Flat modules and Their Homological Dimensions
Wei Qi, Xiaolei Zhang, Wei Zhao
In this paper, we introduce and study the notion of strongly --flat modules. The --weak global dimension --w.gl.dim of an NP-ring is also introduced and…
Strongly -flat modules, strongly nonnil-injective modules and their homological dimensions
Xiaolei Zhang, Shiqi Xing, Wei Qi
In this paper, we first introduce and study the notions of strongly -flat modules and strongly nonnil-injective modules. And then, we investigate the homology dimensions of modu…
Characterizing -Artinianness by uniformity
Xiaolei Zhang, Wei Qi
Let be a commutative ring with identity and a multiplicative subset of . An -module is said to be a uniformly -Artinian (--Artinian for abbreviation) mod…
Some remarks on Lucas modules
Xiaolei Zhang, Guocheng Dai, Wei Qi
In this paper, we discuss some properties on Lucas modules. In details, we show that direct and inverse limits of Lucas modules are Lucas modules, and every -module has a Lucas…
On Cohen's theorem for Artinian modules
Xiaolei Zhang, Hwankoo Kim, Wei Qi
In this paper, we prove that a finitely embedded -module is Artinian if and only if for every prime ideal of with , there e…
On two versions of Cohen's theorem for modules
Xiaolei Zhang, Hwankoo Kim, Wei Qi
Parkash and Kour obtained a new version of Cohen's theorem for Noetherian modules, which states that a finitely generated -module is Noetherian if and only if for every prim…
Uniformly -Noetherian rings
Wei Qi, Hwankoo Kim, Fanggui Wang +2
Let be a ring and a multiplicative subset of . Then is called a uniformly -Noetherian (--Noetherian for abbreviation) ring provided there exists an element…
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…
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 -…