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The primitive element theorem for differential fields with zero derivation on the ground field (1409.3847v3)
Published 12 Sep 2014 in math.RA
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 $F \subset E$, $trdeg_F E < \infty$, and $F$ contains a nonconstant, i.e. an element $f$ such that $f{\prime} \neq 0$, 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 $E$.