15 papers
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…
Almost coherent rings
Xiaolei Zhang
Inspired from the work of P. Scholze on the finiteness of \(\mathbf{F}_{p}\)-cohomology groups of proper rigid-analytic varieties over \(p\)-adic fields, Zavyalov recently introduc…
Rings with uniformly S-w-Noetherian spectrum
Xiaolei Zhang
In this paper, the notion of rings with uniformly S-w-Noetherian spectrum is introduced. Several characterizations of rings with uniformly S-w-Noetherian spectrum are given. Actual…
On S-(h-)divisible modules and their S-strongly flat covers
Xiaolei Zhang
It was proved in [3] that every h-divisible modules admits an strongly flat cover over all integral domains; and every divisible module over an integral domain R admits a strongly…
On the existence of parameterized noetherian rings
Xiaolei Zhang
A ring is called left strictly -noetherian if is the minimum cardinal such that every ideal of is -generated. In this note, we show tha…
Characterizing categoricity in the class
Xiaolei Zhang
We study categoricity of the additive closure , consisting of all direct summands of arbitrary direct sums of copies of a fixed module . For an -genera…
Some new module-theoretic characterizations of -coherent rings
Xiaolei Zhang
Let be a commutative ring with identity and a multiplicative subset of . In this paper, we first introduce and study the notions of -pure exact sequences and -abso…
The Schröder-Bernstein problem for relative injective modules
Xiaolei Zhang
Let be a pair satisfying some mild condition, where is a class of -modules and is a class of -homomorphisms. We show that if and $g:B\right…
Some remarks on injective envelopes on ring extensions
Xiaolei Zhang
Let be a ring extension. We introduce and study the properties of -injective modules and the existences of -injective envelopes. Besi…
A note on -flat preenvelopes
Xiaolei Zhang
In this note, we investigate the notion of -flat preenvelopes of modules. In particular, we give an example that a ring being coherent does not imply that every -module h…
A note on the -version of Noetherianity
Xiaolei Zhang
It is well-known that a ring is Noetherian if and only if every ascending chain of ideals is stationary, and an integral domain is a PID if and only if every countably generated id…
A note on -coherent rings
Xiaolei Zhang
In this note, we show that a ring is -coherent if and only if every finitely presented -module is -coherent, providing a positive answer to a question proposed in [D.…
-Krull dimension of commutative rings
Xiaolei Zhang
In this paper, we introduce and study the -Krull dimension of a commutative ring via its -operation. A new characterization of -von Neumann regular rings is obtained, an…
The small finitistic dimensions of commutative rings, II
Xiaolei Zhang
The small finitistic dimension $\fPD(R)$ of a ring is defined to be the supremum of projective dimensions of -modules with finite projective resolutions. In this paper, we i…
A note on the localization of generalized injective modules
Xiaolei Zhang
Let be a ring and a multiplicative subset of . In this note, we study the localization of -injective modules and --injective modules under -Noetherian rings…