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A pure subalgebra of a finitely generated algebra is finitely generated


Author: Mitsuyasu Hashimoto
Journal: Proc. Amer. Math. Soc. 133 (2005), 2233-2235
MSC (2000): Primary 13E15
DOI: https://doi.org/10.1090/S0002-9939-05-07967-0
Published electronically: March 17, 2005
MathSciNet review: 2138864
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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: https://doi.org/10.1090/S0002-9939-05-07967-0
Keywords: Pure subalgebra, finite generation, flattening.
Received by editor(s): December 30, 2003
Published electronically: March 17, 2005
Communicated by: Bernd Ulrich
Article copyright: © Copyright 2005 American Mathematical Society
The copyright for this article reverts to public domain 28 years after publication.

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