### 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 |

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### ASJC Scopus subject areas

- Mathematics(all)

### Cite this

**CANONICAL and n-CANONICAL MODULES of A NOETHERIAN ALGEBRA.** / Hashimoto, Mitsuyasu.

Research output: Contribution to journal › Article

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

}

TY - JOUR

T1 - CANONICAL and n-CANONICAL MODULES of A NOETHERIAN ALGEBRA

AU - Hashimoto, Mitsuyasu

PY - 2017/6/1

Y1 - 2017/6/1

N2 - 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.

AB - 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.

UR - http://www.scopus.com/inward/record.url?scp=85020639880&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=85020639880&partnerID=8YFLogxK

U2 - 10.1017/nmj.2016.44

DO - 10.1017/nmj.2016.44

M3 - Article

VL - 226

SP - 165

EP - 203

JO - Nagoya Mathematical Journal

JF - Nagoya Mathematical Journal

SN - 0027-7630

ER -