Canonical forms for local derivations

Maxwell Alexander Rosenlicht

Vol. 42 (1972), No. 3, 721–732

DOI: 10.2140/pjm.1972.42.721

Abstract

Consider a field k, the formal power series field k((x)) in one variable over k, and a derivation D of k((x)) that maps k into itself. We wish to replace x by another generator y of k((x)) so that Dy has a particularly simple expression as a function of y. This is accomplished subject to certain restrictions on the differential field k, some deductions are drawn, and there are extensions to the analogous problem for power series rings in several variables.

Mathematical Subject Classification 2000

Primary: 13B10

Milestones

Received: 3 April 1972

Published: 1 September 1972