### Abstract

We prove the following. Let R be a Noetherian commutative ring, B a finitely generated R-algebra, and A a pure R-subalgebra of B. Then A is finitely generated over R.

Original language | English |
---|---|

Pages (from-to) | 2233-2235 |

Number of pages | 3 |

Journal | Proceedings of the American Mathematical Society |

Volume | 133 |

Issue number | 8 |

DOIs | |

Publication status | Published - Aug 2005 |

Externally published | Yes |

### Fingerprint

### Keywords

- Finite generation
- Flattening
- Pure subalgebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

### Cite this

**A pure subalgebra of a finitely generated algebra is finitely generated.** / Hashimoto, Mitsuyasu.

Research output: Contribution to journal › Article

*Proceedings of the American Mathematical Society*, vol. 133, no. 8, pp. 2233-2235. https://doi.org/10.1090/S0002-9939-05-07967-0

}

TY - JOUR

T1 - A pure subalgebra of a finitely generated algebra is finitely generated

AU - Hashimoto, Mitsuyasu

PY - 2005/8

Y1 - 2005/8

N2 - We prove the following. Let R be a Noetherian commutative ring, B a finitely generated R-algebra, and A a pure R-subalgebra of B. Then A is finitely generated over R.

AB - We prove the following. Let R be a Noetherian commutative ring, B a finitely generated R-algebra, and A a pure R-subalgebra of B. Then A is finitely generated over R.

KW - Finite generation

KW - Flattening

KW - Pure subalgebra

UR - http://www.scopus.com/inward/record.url?scp=23744488312&partnerID=8YFLogxK

UR - http://www.scopus.com/inward/citedby.url?scp=23744488312&partnerID=8YFLogxK

U2 - 10.1090/S0002-9939-05-07967-0

DO - 10.1090/S0002-9939-05-07967-0

M3 - Article

VL - 133

SP - 2233

EP - 2235

JO - Proceedings of the American Mathematical Society

JF - Proceedings of the American Mathematical Society

SN - 0002-9939

IS - 8

ER -