2015/08/30 by Mitsuyasu Hashimoto, Hashimoto, Mitsuyasu
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Commutative Algebra (math.AC) #Commutative Algebra and Its Applications #FOS: Mathematics #Primary 16E05 #Rings and Algebras (math.RA) #Secondary 16E65 #math.AC #math.RA #msc:16E05 #msc:16E65
paper · pdf · doi:10.48550/arxiv.1508.07552
49 pages
arxiv created 2015/08/30 · openalex publication_date 2015/08/30 · arxiv updated 2015/09/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
We define canonical and n-canonical modules on a module-finite algebra over a Noether commutative ring and study their basic properties. Using n-canonical modules, we generalize a theorem on (n,C)-syzygy by Araya and Iima which generalize a well-known theorem on syzygies by Evans and Griffith. Among others, we prove a non-commutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism. We also prove the codimension two-argument for modules over a coherent sheaf of algebras with a 2-canonical module, generalizing a result of the author.