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

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⊂E, trdegFE<∞, and F contains a nonconstant, i.e., an element f such that f′≠0, then there exists a∈E such that E is generated by a and F. We replace the last condition with the existence of a nonconstant element in E.