  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. An application to the problems of local, $k$-local
derivations(automorphisms) of finite dimensional algebras is provided as well.
