On higher derivations: a survey. (English) Zbl 1234.16030

Let \(R\) be a ring and \(D=\{d_i\mid i=0,1,\dots,n,\dots\}\) a sequence of additive mappings on \(R\) such that \(d_0=\text{id}\). Then \(D\) is called a higher derivation if for all \(n\geq 1\), \(d_n(ab)=\sum^n_{i=0} d_i(a)d_{n-1}(b)\) for all \(a,b\in R\).
The authors give a historical survey of results on higher derivations and some generalizations, and they state some open problems. The list of references includes 100 items.


16W25 Derivations, actions of Lie algebras
16-02 Research exposition (monographs, survey articles) pertaining to associative rings and algebras
01A60 History of mathematics in the 20th century
16-03 History of associative rings and algebras