11 papers · 1 filter
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…
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…
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…