2008/08/04 by Zhe Dong, Dong, Z. -C., Q.-S. Wu +1 · 1 citation
Computer Science · Mathematics · #14A22 #16E30 #16E65 #16W50 #Advanced Algebra and Logic #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #Commutative Algebra and Its Applications #FOS: Mathematics #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.0808.0407
openalex publication_date 2008/08/04 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
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 the Castelnuovo-Mumford regularity and the Ext-regularity coincide for all finitely generated A-modules. This can be viewed as a non-commutative version of \cite[Theorem 1.3]ro. By using Castelnuovo-Mumford regularity, we prove that any Koszul standard AS-Gorenstein algebra is AS-regular. As a preparation to prove the main result, we also prove the following statements are equivalent: (1) A is AS-Gorenstein; (2) A has finite left injective dimension; (3) the dualizing complex has finite left projective dimension. This generalizes \cite[Corollary 5.9]mori.