Lie extensions (Q1385023)

The author introduces a new type of differential field extensions -- Lie extensions. As opposed to Kolchin's strongly normal extensions, Lie extensions are defined in an inner manner and form a more extensive class of differential extensions as follows from the theorem: Suppose that \(K\) is algebraically closed. Then every intermediate differential field of a strongly normal extension of \(K\) is a Lie extension of \(K\). We note that in this connection there is a certain need in formal algebraic theory for describing classical results for algebraic differential equations with general solutions without movable singularities [\textit{K. Nishioka}, Hokkaido Math. J. 25, 453-463 (1996; Zbl 0886.12004)]. A suitable definition of an extension for a differential field [see points (i--ii) of the reviewer's note to the review for \textit{H. Umemura}, Nagoya Math. J. 144, 1-58 (1996; Zbl 0885.12004)] is needed.