A note on finite dimensional subrings of polynomial rings

Author:
Paul Eakin

Journal:
Proc. Amer. Math. Soc. **31** (1972), 75-80

MathSciNet review:
0289498

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Abstract | References | Additional Information

Abstract: Let be a field and a family of indeterminates over . We show that if is a ring of Krull dimension such that then there are elements which are algebraically independent over and a -isomorphism such that . This is used to show that a onedimensional ring which satisfies the above conditions is necessarily an affine ring over and is necessarily a polynomial ring if it is normal. In addition we show that such a ring is a normal affine ring of transcendence degree two over if and only if it is a two-dimensional Krull ring such that each essential valuation of has residue field transcendental over .

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Additional Information

DOI:
https://doi.org/10.1090/S0002-9939-1972-0289498-2

Keywords:
Dedekind domain,
Krull ring,
polynomial ring,
affine ring,
noetherian ring,
Krull dimension

Article copyright:
© Copyright 1972
American Mathematical Society