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A pure subalgebra of a finitely generated algebra is finitely generated

Author(s): Mitsuyasu Hashimoto
Journal: Proc. Amer. Math. Soc. 133 (2005), 2233-2235.
MSC (2000): Primary 13E15
Posted: March 17, 2005
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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 $R$.

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Additional Information:

Mitsuyasu Hashimoto
Affiliation: Graduate School of Mathematics, Nagoya University, Chikusa-ku, Nagoya 464--8602, Japan
Email: hasimoto@math.nagoya-u.ac.jp

DOI: 10.1090/S0002-9939-05-07967-0
PII: S 0002-9939(05)07967-0
Keywords: Pure subalgebra, finite generation, flattening.
Received by editor(s): December 30, 2003
Posted: March 17, 2005
Communicated by: Bernd Ulrich
Copyright of article: Copyright 2005, American Mathematical Society
The copyright for this article reverts to public domain after 28 years from publication.

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