  Let $\mathcal A$ and $\mathcal B$ be two (complex) algebras. A linear map
$\phi:{\mathcal A}\to{\mathcal B}$ is called $n$-homomorphism if $\phi(a_{1}...
a_{n})=\phi(a_{1})...\phi(a_{n})$ for each $a_{1},...,a_{n}\in{\mathcal A}.$ In
this paper, we investigate $n$-homomorphisms and their relation to
homomorphisms. We characterize $n$-homomorphisms in terms of homomorphisms
under certain conditions. Some results related to continuity and commutativity
are given as well.
