English (United Kingdom)

https://curated-unify.zendy.io/wp-json/zendy-region/v1/featured_content/oa?rat=en

https://curated-unify.zendy.io/wp-json/zendy-region/v1/highlighted_journal/

Global: Zendy Plus annual

Presents the access of premium content as premium feature

Premium Content

Presents the keyphrase highlighting as premium feature

Keyphrase Highlighting

Presents the summarisation as premium feature

Summarisation

Insights

Presents the pdf analysis as premium feature

PDF Analysis

Presents the zaia usage as premium feature

ZAIA

Global: Zendy Plus monthly

Global: Zendy Tools annual

Global: Zendy Tools monthly

Global: Zendy Free Plan

Let $A$ be a connected graded $k$-algebra with a balanced dualizing complex.We prove that $A$ is a Koszul AS-regular algebra if and only if that theCastelnuovo-Mumford regularity and the Ext-regularity coincide for all finitelygenerated $A$-modules. This can be viewed as a non-commutative version of\cite[Theorem 1.3]{ro}. By using Castelnuovo-Mumford regularity, we prove thatany Koszul standard AS-Gorenstein algebra is AS-regular. As a preparation toprove the main result, we also prove the following statements are equivalent:(1) $A$ is AS-Gorenstein; (2) $A$ has finite left injective dimension; (3) thedualizing complex has finite left projective dimension. This generalizes\cite[Corollary 5.9]{mori}.

Non-commutative Castelnuovo-Mumford Regularity and AS-regular Algebras