8 papers
Quotient Morita Theory with Applications
Xuyang Chen, Haonan Li, Quanshui Wu
We study equivalences between quotient categories of module categories associated with Gabriel topologies. We establish necessary and sufficient conditions for a Morita context to…
Noncommutative resolutions of noncommutative isolated singularities
Haonan Li, Quanshui Wu
Noncommutative resolutions of AS-Gorenstein isolated singularities are investigated by Li--Shen--Wu. However, establishing their existence and constructing such resolutions are gen…
Connected Hopf Algebras that are Not Hopf Ore Extensions of Enveloping Algebras
Mengying Hu, Quanshui Wu
We construct a family of connected Hopf algebras with finite Gelfand-Kirillov dimension, none of which is an iterated Hopf Ore extension of the universal enveloping algebra of its…
Commonly Graded Algebras and Their Homological Properties
Haonan Li, Quanshui Wu
In this article, we study bounded-below locally finite -graded algebras, which are referred to as commonly graded algebras in literature. Commonly graded algebras have…
Numerical homological regularities over positively graded algebras
Quanshui Wu, Bojuan Yi
We study numerical regularities for complexes over noncommutative noetherian locally finite -graded algebras such as CM (cm)-regularity, Tor (tor)-regularity (Ext (…
Noncommutative resolutions of AS-Gorenstein isolated singularites
Haonan Li, Menda Shen, Quanshui Wu
In this paper, we investigate noncommutative resolutions of (generalized) AS-Gorenstein isolated singularities. Noncommutative resolutions in graded case are achieved as the graded…
Regular -graded local rings and Graded Isolated Singularities
Haonan Li, Quanshui Wu
In this note we first study regular -graded local rings. We characterize commutative noetherian regular -graded local rings in similar ways as in the usual…
Generalized Koszul Algebra and Koszul Duality
Haonan Li, Quanshui Wu
We define generalized Koszul modules and rings and develop a generalized Koszul theory for -graded rings with the degree zero part noetherian semiperfect. This theory s…