n-Homomorphisms

Abstract

Let $\mathcal{A}$ and $\mathcal{B}$ be two (complex) algebras. A linear map $\varphi :\mathcal{A}\to \mathcal{B}$ is called $n$-homomorphism if $\varphi (a_1...a_n)=\varphi (a_1)...\varphi (a_n)$ 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.

10 pages, revised paper