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In this note we propose a definition of inner derivation for nonassociative algebras. This definition coincides with the usual one for Lie algebras, and for associative algebras with no absolute right (left) divisor of zero. It is well known that all derivations of semi-simple associative or Lie algebras over a field of characteristic zero are inner.Recent correspondence with N. Jacobson has revealed that a number of the ideas in this note duplicate some of his current researches.1 In particular, he has shown that every derivation of a semisimple non-associative algebra (that is, direct sum of simple algebras) with a unity quantity over a field of characteristic zero is inner in this sense. Preliminaries.A derivation of a non-associative algebra 21 over a field % is a linear transformation D on 2Ï satisfyingfor all x, y in 21. It is known [2] 2 that the set 3) of all derivations of 21 is a Lie algebra over g if multiplication in 2) is defined by

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