Kyoto Journal of Mathematics

Small embeddings of integral domains

Yu Yang Bao and Daniel Daigle

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Abstract

Let A be a geometrically integral algebra over a field k. We prove that, for any affine k-domain R, if there exists an extension field K of k such that RKkA and RK, then there exists an extension field L of k such that RLkA and trdegk(L)<trdegk(R). This generalizes a result of Freudenburg, namely, the fact that this is true for A=k[1].

Article information

Source
Kyoto J. Math., Volume 59, Number 3 (2019), 703-716.

Dates
Received: 4 August 2016
Revised: 5 April 2017
Accepted: 16 May 2017
First available in Project Euclid: 21 May 2019

Permanent link to this document
https://projecteuclid.org/euclid.kjm/1558404168

Digital Object Identifier
doi:10.1215/21562261-2019-0022

Mathematical Reviews number (MathSciNet)
MR3990183

Zentralblatt MATH identifier
07108008

Subjects
Primary: 14R10: Affine spaces (automorphisms, embeddings, exotic structures, cancellation problem)
Secondary: 13B25: Polynomials over commutative rings [See also 11C08, 11T06, 13F20, 13M10] 13G05: Integral domains

Keywords
integral domains tensor products ring extensions

Citation

Bao, Yu Yang; Daigle, Daniel. Small embeddings of integral domains. Kyoto J. Math. 59 (2019), no. 3, 703--716. doi:10.1215/21562261-2019-0022. https://projecteuclid.org/euclid.kjm/1558404168


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