On Hasse-Schmidt higher derivations
On Hasse-Schmidt higher derivations
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DOI：
10.18910/9183
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发表时间：
1986
影响因子：
0.4
通讯作者：
Sadi Abu Saymeh
中科院分区：
文献类型：
--
作者：
Sadi Abu Saymeh
£= {D0,DlyD2y…}的可加性Λ-endomorphisms Z)/s，使得Z)o是4和n Dn（ab)= 2 J A»（tf） DnJb）的恒等映射，对于每个β， b^A。H. Hasse和F.K. Schmidt在1986年提出了高m = 0导数这个有趣的概念。本文证明了a / k的高阶导数D唯一地表示为a / k的某一阶导数序列。设nir为正整数，使得n>r。我们用Pnr表示n有序划分为r个正整数的集合，即：
£ = {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.,