Characterization of $n$-Jordan Homomorphisms on Rings | Zendy

Abbas Zivari-Kazempour | Zendy; Mohammad Valaei | Zendy

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Characterization of $n$-Jordan Homomorphisms on Rings

Author(s) -

Abbas Zivari-Kazempour,

Mohammad Valaei

Publication year - 2021

Publication title -

tamkang journal of mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.324

H-Index - 18

eISSN - 0049-2930

pISSN - 2073-9826

DOI - 10.5556/j.tkjm.53.2022.3644

Subject(s) - homomorphism , mathematics , unit (ring theory) , characterization (materials science) , algebra homomorphism , combinatorics , algebra over a field , discrete mathematics , pure mathematics , mathematics education , physics , optics

In this paper, we prove that if $\varphi:\mathcal{R}\longrightarrow\mathcal{R}'$ is an $n$-Jordan homomorphism, where $\mathcal{R}$ has a unit $e$, then the map $a\longmapsto \varphi(e)^{n-2}\varphi(a)$ is a Jordan homomorphism. As a consequence we show, under special hypotheses, that each $n$-Jordan homomorphism is an $n$-homomorphism.

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