Characterization of $n$-Jordan Homomorphisms on Rings

Authors

  • Abbas Zivari-kazempour Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran. https://orcid.org/0000-0001-8362-8490
  • Mohammad Valaei Department of Mathematics, Ayatollah Borujerdi University, Borujerd, Iran.

DOI:

https://doi.org/10.5556/j.tkjm.53.2022.3644

Keywords:

$n$-homomorphism, $n$-Jordan homomorphism, semisimple.

Abstract

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.

References

G. Ancochea, Le thtorime de von Staudt en geometrie projective quaiernionienne, J. Reine Angew. Math., 184 (1942), 192-198.

G. An, Characterization of $n$-Jordan homomorphism, Linear Multi. Algebra, 66(4), (2018), 671-680.

A. Bodaghi and H. .{I}nceboz, $n$-Jordan homomorphisms on commutative algebras, Acta. Math. Univ. Comenianae., 87(1), (2018), 141-146 .

J. Bračič and M. S. Moslehian, On automatic continuity of $3$-homomorphisms on Banach algebras, Bull. Malaysian Math. Sci. Soc., 30(2), (2007), 195-200.

Sh. Hejazian, M. Mirzavaziri and M. S. Moslehian, $n$-homomorphisms, Bull. Iranian Math. Soc., 31(1), (2005), 13-23.

I. N. Herstein, Jordan homomorphisms, Trans. Amer. Math. Soc., 81(1), (1956), 331-341.

N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc., 69(3), (1950), 479-502.

I. Kaplansky, Semi-automorphisms of rings, Duke Math. J. vol. 14 (1947), 521-527.

T. Miura, S. E. Takahasi and G. Hirasawa, Hyers-Ulam-Rassias stability of Jordan homomorphisms on Banach algebras, J. Ineq. Appl., 2005(4), (2005), 435-441.

W. Zelazko, A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math., 30 (1968), 83-85.

A. Zivari-Kazempour, A characterization of $3$-Jordan homomorphism on Banach algebras, Bull. Aust. Math. Soc., 93(2), (2016), 301-306.

A. Zivari-Kazempour, Automatic continuity of $n$-Jordan homomorphisms on Banach algebras, Commun. Korean Math. Soc., 33(1), (2018), 165-170.

A. Zivari-Kazempour, A characterization of Jordan and $5$-Jordan homomorphisms between Banach algebras, Asian. Eur. J. Math., 11(2), (2018), 1–10.

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Published

2021-11-14 — Updated on 2022-01-25

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How to Cite

Zivari-kazempour, A., & Valaei, M. (2022). Characterization of $n$-Jordan Homomorphisms on Rings. Tamkang Journal of Mathematics, 53(1), 89-96. https://doi.org/10.5556/j.tkjm.53.2022.3644 (Original work published November 14, 2021)

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