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n-Homomorphisms

S. Hejazian·M. Mirzavaziri·M. S. Moslehian
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Abstract

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.

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S. Hejazian, M. Mirzavaziri, M. S. Moslehian. 2004-06-27. n-Homomorphisms. https://arxiv.org/abs/math/0406553

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