Haetinger, Claus; Ashraf, Mohammad; Ali, Shakir On higher derivations: a survey. (English) Zbl 1234.16030 Int. J. Math. Game Theory Algebra 19(2010), No. 5-6, 359-379 (2011). 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. Reviewer: Howard E. Bell (St. Catharines) Cited in 5 Documents 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 Keywords:additive maps; generalized higher derivations; generalized Jordan higher derivations PDFBibTeX XMLCite \textit{C. Haetinger} et al., Int. J. Math. Game Theory Algebra 19, No. 5--6, 359--379 (2011; Zbl 1234.16030)