Vol. 15, No. 1, 1965

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A new measure of a partial differential field extension

Israel Zuckerman

Vol. 15 (1965), No. 1, 357–371

Let G be a differential field of characteristic zero with the commuting derivations d1,,dm. If F is a differential subfield of G, the algebraic and differential degrees of transcendence of G over F, denoted respectively by d(GF) and d.d(GF) are numerical invariants of the extension. Unlike the ordinary differential case (m = 1) d.d.(GF) = 0 does not imply that d(GF) is finite. In this paper an intermediate measure of the extension is constructed, called the limit vector. The first and last components of this vector correspond to d.d(GF) and d(GF) respectively, and the limit vector is additive.

Mathematical Subject Classification
Primary: 12.80
Received: 23 January 1964
Published: 1 March 1965
Israel Zuckerman