Derivations in Semigroup Algebras

Abstract

The main goal of this paper is to describe derivations in semigroup algebras, where the semigroup satisfies the Maltsev conditions. We prove that the derivation algebra of such semigroup algebra is embedded into the derivation algebra of some group. In addition, we describe the so-called quasi-inner derivations as an ideal in a derivation algebra, which is useful for the further study of differentiations in semigroup algebras.