Open AccessCharacterization 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.