Communications of the
Korean Mathematical Society CKMS

In this short note, we give a simple proof of the main theorem of \cite{Cheshmavar} which states that every $n$-Jordan homomorphism $h:A\longrightarrow B$ between two commutative algebras $A$ and $B$ is an $n$-homomorphism.

Keywords: $n$-ring homomorphism, $n$-Jordan homomorphism, commutative ring

MSC numbers: Primary 47B48; Secondary 46L05, 46H25