**DIPS 6/96**[tex source, PostScript, dvi]**Title:**Field extensions and extensions of linear differential operators**Author:**Michael M. VinogradovLet $K\subset R\subset P$ be a tower of fields, $N$ be a $P$-module, and $\Delta : R\to N$ be a $K$-linear differential operator. The aim of this paper is to investigate whether the operator $\Delta$ has an extension to $P$, i.e. if there exists a differential operator $\Dp{}: P\to N$ such that $\Dp{}|_R=\Delta$.

**To appear**in Acta Applicandae Math.10 pages. AmS-TeX, XYpic. To compile source files (

**.tex**) one needs the title page style files titams.tex.