文献类型：期刊文献

英文题名：LIE n-HIGHER DERIVATIONS AND LIE n-HIGHER DERIVABLE MAPPINGS

作者：Ding, Yana[1];Li, Jiankui[1]

机构：[1]East China Univ Sci & Technol, Dept Math, Shanghai, Peoples R China

年份：2017

卷号：96

期号：2

起止页码：223

外文期刊名：BULLETIN OF THE AUSTRALIAN MATHEMATICAL SOCIETY

收录：;WOS:【SCI-EXPANDED(收录号:WOS:000411403100007)】；

基金：This work is partially supported by the National Natural Science Foundation of China, Grant No. 11371136.

语种：英文

外文关键词：Lie higher derivation; Lie n-higher derivable mapping; Lie n-higher derivation; Lie triple higher derivation

摘要：Let A be a unital torsion-free algebra over a unital commutative ring R. To characterise Lie n-higher derivations on A, we give an identity which enables us to transfer problems related to Lie n-higher derivations into the same problems concerning Lie n-derivations. We prove that: (1) if every Lie n-derivation on A is standard, then so is every Lie n-higher derivation on A; (2) if every linear mapping Lie n-derivable at several points is a Lie n-derivation, then so is every sequence {d(m)} of linear mappings Lie n-higher derivable at these points; (3) if every linear mapping Lie n-derivable at several points is a sum of a derivation and a linear mapping vanishing on all (n - 1) th commutators of these points, then every sequence {d(m)} of linear mappings Lie n-higher derivable at these points is a sum of a higher derivation and a sequence of linear mappings vanishing on all (n - 1) th commutators of these points. We also give several applications of these results.