On (n,m)-Jordan homomorphisms on algebras

Masoumeh Neghabi, Abasalt Bodaghi, Abbas Zivari-Kazempour


In this paper, we show that every $(n,m)$-Jordan homomorphism between two commutative algebras is an $(n,m)$-homomorphism. For the non-commutative case, we prove that every surjective $(2,m)$-Jordan homomorphism from an algebra $\mathcal{A}$ to a semiprime commutative algebra $\mathcal{B}$ is $(2,m)$-homomorphism.


$n$-homomorphism, $n$-Jordan homomorphism, mixed $n$-Jordan homomorphism, automatic continuity, semisimple

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