CANONICAL AND n-CANONICAL MODULES OF A NOETHERIAN ALGEBRA

We define canonical and n-canonical modules of 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 noncommutative version of Aoyama's theorem which states that a canonical module descends with respect to a flat local homomorphism.