## 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.

### MSC:

 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