A remark on $n-$Jordan homomorphisms

TL;DR

This paper proves that in the context of commutative algebras, every n-Jordan homomorphism is also an n-homomorphism, clarifying the relationship between these algebraic structures.

Contribution

It establishes that n-Jordan homomorphisms coincide with n-homomorphisms for commutative algebras, providing a key insight into their structural equivalence.

Findings

n-Jordan homomorphisms are n-homomorphisms in commutative algebras

The result simplifies understanding of algebraic mappings in commutative settings

Clarifies the relationship between different types of algebra homomorphisms

Abstract

Let $A$ and $B$ be commutative algebras and $n\geqslant 2$ an integer. Then each $n-$ Jordan homomorphism $h:A\rightarrow B$ is an $n-$homomorphism.