The primitive element theorem for differential fields with zero derivation on the ground field

Gleb A. Pogudin

doi:10.1016/j.jpaa.2015.02.004.

paper

The primitive element theorem for differential fields with zero derivation on the ground field

arXiv:1409.3847 · doi:10.1016/j.jpaa.2015.02.004.

Abstract

In this paper we strengthen Kolchin's theorem ([1]) in the ordinary case. It states that if a differential field $E$ is finitely generated over a differential subfield $F \subset E$ , $t r d e g_{F} E < \infty$ , and $F$ contains a nonconstant, i.e. an element $f$ such that $f^{'} \neq = 0$ , then there exists $a \in E$ such that $E$ is generated by $a$ and $F$ . We replace the last condition with the existence of a nonconstant element in $E$ .

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