On a certain extensions of linear spaces with an algebraic derivation

Abstract

Certain properties of solutions of ordinary line ar differential equations have an algebraic character. In this note we a re concerned with these properties. Our purpose is to show some connections between the theory of differential rings and the theory of lin e ar spaces equipped w ith an endomorphism s a tisfying some additional conditions. It will be shown th a t some lin e ar spaces may be extended to diffe rentia l rings.