## Kyoto Journal of Mathematics

### Small embeddings of integral domains

#### 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 $R\subseteq K\otimes_{k}A$ and $R\nsubseteq K$, then there exists an extension field $L$ of $k$ such that $R\subseteqL\otimes_{k}A$ and $\operatorname{trdeg}_{k}(L)\lt \operatorname{trdeg}_{k}(R)$. 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
Revised: 5 April 2017
Accepted: 16 May 2017
First available in Project Euclid: 21 May 2019

https://projecteuclid.org/euclid.kjm/1558404168

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

Mathematical Reviews number (MathSciNet)
MR3990183

Zentralblatt MATH identifier
07108008

#### 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