Acta Mathematica Academiae Paedagogicae Nyíregyháziensis, Vol. 29, pp. 67-74 (2013)

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On $\sigma$-derivations on finite matrix algebras

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Ana P. Madrid

Facultad de Ciencias Exactas, NUCOMPA

**Abstract:** Our aim is to characterize the class $D(\sigma)$ of $\sigma$-derivations on finite matrix algebras. Nevertheless the full description of $\sigma$-derivations is quite difficult, even in the finite dimensional case, the problem has its own interest. We will prove that $D(\sigma)$ consists of the solution of some linear system of matrix equations. Some posed questions concerning the structure of $\sigma$-derivations will also be considered.

**Keywords:** $\sigma$-derivations. Matrix algebras. Algebraic homomorphisms. Linear system of matricial equations

**Classification (MSC2000):** 47B47; 47B48

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