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September 2015 An affine version of a theorem of Nagata
Gene Freudenburg
Kyoto J. Math. 55(3): 663-672 (September 2015). DOI: 10.1215/21562261-3089136


Let R be an affine k-domain over the field k. The paper’s main result is that if R admits a nontrivial embedding in a polynomial ring K[s] for some field K containing k, then R can be embedded in a polynomial ring F[t] which extends R algebraically. This theorem can be applied to subrings of a ring which admits a nonzero locally nilpotent derivation. In this way, we obtain a concise new proof of the cancellation theorem for rings of transcendence degree one for fields of characteristic 0.


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Gene Freudenburg. "An affine version of a theorem of Nagata." Kyoto J. Math. 55 (3) 663 - 672, September 2015.


Received: 23 May 2014; Revised: 18 August 2014; Accepted: 25 August 2014; Published: September 2015
First available in Project Euclid: 9 September 2015

zbMATH: 1339.14032
MathSciNet: MR3395985
Digital Object Identifier: 10.1215/21562261-3089136

Primary: 13B25 , 14R10

Keywords: cancellation problem , Locally nilpotent derivation , Lüroth theorem

Rights: Copyright © 2015 Kyoto University


Vol.55 • No. 3 • September 2015
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