### Abstract

We define canonical and -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.

Original language | English |
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Pages (from-to) | 165-203 |

Number of pages | 39 |

Journal | Nagoya Mathematical Journal |

Volume | 226 |

DOIs | |

Publication status | Published - Jun 1 2017 |

### ASJC Scopus subject areas

- Mathematics(all)

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## Cite this

Hashimoto, M. (2017). CANONICAL and n-CANONICAL MODULES of A NOETHERIAN ALGEBRA.

*Nagoya Mathematical Journal*,*226*, 165-203. https://doi.org/10.1017/nmj.2016.44