### 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 |
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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 1 2005 |

### Keywords

- Finite generation
- Flattening
- Pure subalgebra

### ASJC Scopus subject areas

- Mathematics(all)
- Applied Mathematics

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## Cite this

Hashimoto, M. (2005). A pure subalgebra of a finitely generated algebra is finitely generated.

*Proceedings of the American Mathematical Society*,*133*(8), 2233-2235. https://doi.org/10.1090/S0002-9939-05-07967-0