On Hasse-Schmidt higher derivations
Sadi Abu Saymeh · Osaka City University (Osaka City University) · 1986
£ = {D0,DlyD2y ...} of additive Λ-endomorphisms Z)/s such that Z)o is the identity map of 4 and n Dn(ab)= 2 J A»(tf) DnJb) for every β, b^A. This interesting notion of higher m = 0 derivations was introduced by H. Hasse and F.K. Schmidt in [1]. In this paper we shall prove that a higher derivation D of A over k is represented uniquely by a certain sequence of derivations of A over k. Let nyr be positive integers such that n>r. We shall denote by Pnr the set of ordered partitions of n into r-positive integers, i.e.,