2 citations · 3 across the 9 of their papers we have counts for
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The small finitistic dimensions of commutative rings, III
Xiaolei Zhang
The small finitistic dimension fPD of a ring is defined to be the supremum of projective dimensions of -modules with finite projective resolutions. In this paper, we sh…
Relative Faithful Exact Functors and Their Applications to Homological Modules
Xiaolei Zhang, Lei Qiao, Hwankoo Kim
The notions of faithfully projective, faithfully flat, and faithfully injective modules--defined as modules for which the three classical homological functors are both faithful and…
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…
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…
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…