$n$-Jordan homomorphisms on C-algebras

Subject Areas : History and biography

A. Bodaghi ¹ , B. Shojaee ²

1 - Department of Mathematics, Garmsar Branch, Islamic Azad University, Garmsar, Iran
2 - Department of Mathematics, Karaj Branch, Islamic Azad University, Karaj, Iran

Received: 2015-04-12 Accepted : 2015-04-12 Published : 2012-03-01

Keywords: n-homomorphism, n-ring,

Abstract :

Let $n\in \mathbb{N}$. An additive map $h:A\to B$ between algebras $A$ and $B$ is called $n$-Jordan homomorphism if $h(a^n)=(h(a))^n$ for all $a\in A$. We show that every $n$-Jordan homomorphism between commutative Banach algebras is a $n$-ring homomorphism when $n < 8$.For these cases, every involutive $n$-Jordan homomorphism between commutative C-algebrasis norm continuous.

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