On finite dimensional algebras with trivial derivation (automorphism)

This paper deals with n dimensional algebras, over any field, which have only trivial derivation (automorphism). It is shown that the corresponding sets of algebras are not empty and in algebraically closed field case they are dense subsets of the variety of n dimensional algebras with respect to the Zariski topology. Some applications to the problems of local, k-local derivations(automorphisms) of finite dimensional algebras are provided as well.