6 papers
Duality Between Injective Envelopes and Flat Covers over Noether Algebras
Xiaolei Zhang
It follows by Puuska that, over a commutative Noetherian ring , a morphism of -modules is an injective envelope if and only if its Matlis dual $Hom_R(i,…
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…
Characterizing Baer Modules Over -Semisimple Rings: An Extension of Baer's Problem
Xiaolei Zhang, Hwankoo Kim
In this note, we investigate the Baer splitting problem over commutative rings. In particular, we show that if a commutative ring is -semisimple, then every Baer -modu…
On (uniformly) --Noetherian rings and modules
Xiaolei Zhang
Let be a ring and a multiplicative subset of . We introduce and study the notions of (-)--Noetherian modules and (-)--principal ideal modules. Some cha…
On the generalizations of global dimensions and singularity categories
Xiaolei Zhang, Tiwei Zhao, Dingguo Wang
For each , we introduce the notion of -singularity category of a given ring , which can be seen as a generalization…