A pure subalgebra of a finitely generated algebra is finitely generated

Mitsuyasu Hashimoto

doi:10.1090/S0002-9939-05-07967-0

A pure subalgebra of a finitely generated algebra is finitely generated

Mitsuyasu Hashimoto

Graduate School of Natural Science and Technology

Research output: Contribution to journal › Article › peer-review

6 Citations (Scopus)

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	https://doi.org/10.1090/S0002-9939-05-07967-0
Publication status	Published - Aug 2005

Keywords

Finite generation
Flattening
Pure subalgebra

ASJC Scopus subject areas

Mathematics(all)
Applied Mathematics

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10.1090/S0002-9939-05-07967-0

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title = "A pure subalgebra of a finitely generated algebra is finitely generated",

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.",

keywords = "Finite generation, Flattening, Pure subalgebra",

author = "Mitsuyasu Hashimoto",

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KW - Finite generation

KW - Flattening

KW - Pure subalgebra

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JO - Proceedings of the American Mathematical Society

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A pure subalgebra of a finitely generated algebra is finitely generated

Abstract

Keywords

ASJC Scopus subject areas

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