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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.



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