Derivations of tensor products of nonassociative algebras

Let R and S be nonassociative unital algebras. Assuming that either one of them is finite dimensional or both are finitely generated, we show that every derivation of R circle times S is the sum of derivations of the following three types: (a) ad u where u belongs to the nucleus of R circle times S, (b) L-z circle times f where f is a derivation of S and z lies in the center of R, and (c) g circle times L-w where g is a derivation of R and w lies in the center of S. (C) 2017 Elsevier Inc. All rights reserved.