Canonical Maps to Twisted Rings

2004/09/21 by D. Rogalski, J. J. Zhang, Rogalski, D. +2 · 1 citation
Mathematics · #14A22 #16P90 #16S38 #16W50 #Advanced Topics in Algebra #Algebraic Geometry (math.AG) #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA) #Rings, Modules, and Algebras #math.AG #math.RA #msc:14A22 #msc:16P90 #msc:16S38 #msc:16W50

paper · pdf · doi:10.48550/arxiv.math/0409405

LaTeX, 21 pages; corollary of main theorem added to intro; other minor changes from ver. 1

openalex publication_date 2004/09/21 · arxiv created 2004/12/14 · arxiv updated 2009/12/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

If A is a strongly noetherian graded algebra generated in degree one, then there is a canonically constructed graded ring homomorphism from A to a twisted homogeneous coordinate ring B(X, L, sigma), which is surjective in large degree. This result is a key step in the study of projectively simple rings. The proof relies on some results concerning the growth of graded rings which are of independent interest.

Citations

• Noncommutative Projective Schemes

Cited by

• Point modules of Nichols algebras over non-abelian groups

Related

• Naive blowups and canonical birationally commutative factors
• Algebras in which every subalgebra is noetherian
• On the classification of G-graded twisted algebras
• The Dixmier-Moeglin equivalence for twisted homogeneous coordinate rings
• Twisted Segre products