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 Some results on $n$-Jordan homomorphisms Bull. Korean Math. Soc. 2020 Vol. 57, No. 1, 31-35 https://doi.org/10.4134/BKMS.b180719Published online January 31, 2020 Jahangir Cheshmavar, Seyed Kamel Hosseini, Choonkil Park Payame Noor University; Payame Noor University; Hanyang University Abstract : 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 Downloads: Full-text PDF