Bulletin of the
Korean Mathematical Society BKMS

With the motivation to extend the Zelasko's theorem on commutative algebras, it was shown in \cite{Eshaghi.2009} that if $n \in \{3, 4\}$ is fixed, $A, B$ are commutative algebras and $h:A\rightarrow B$ is an $n$-Jordan homomorphism, then $h$ is an $n$-ring homomorphism. In this paper, we extend this result for all $n\geq 3$.

Keywords: Banach algebra, $n$-Jordan homomorphism, $n$-ring homomorphism, $n$-homomorphism

MSC numbers: Primary 47B48, 46L05, 46H25, 39B52

Supported by: C. Park was supported by Basic Science Research Program through the National Research Foundation of Korea funded by the Ministry of Education, Science and Technology (NRF-2017R1D1A1B04032937)