Communications of the Korean Mathematical Society (대한수학회논문집)

Korean Mathematical Society (대한수학회)
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A SIMPLE PROOF FOR A RESULT ON n-JORDAN HOMOMORPHISMS

  • Choonkil Park (Department of Mathematics Research Institute for Natural Sciences Hanyang University) ;
  • Abbas Zivari-Kazempour (Department of Mathematics Ayatollah Borujerdi University)
  • Received : 2022.05.16
  • Accepted : 2022.07.22
  • Published : 2023.04.30
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Abstract

In this short note, we give a simple proof of the main theorem of [5] which states that every n-Jordan homomorphism h : A → B between two commutative algebras A and B is an n-homomorphism.

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References

  1. G. An, Characterizations of n-Jordan homomorphisms, Linear Multilinear Algebra 66 (2018), no. 4, 671-680. https://doi.org/10.1080/03081087.2017.1318818 
  2. G. Ancochea, Le theoreme de von Staudt en geometrie projective quaternionienne, J. Reine Angew. Math. 184 (1942), 193-198. https://doi.org/10.1515/crll.1942.184.193 
  3. A. Bodaghi and H. Inceboz, n-Jordan homomorphisms on commutative algebras, Acta Math. Univ. Comenian. (N.S.) 87 (2018), no. 1, 141-146. 
  4. A. Bodaghi and B. Shojaee, n-Jordan homomorphisms on C∗-algebras, J. Linear Topol. Algebras. 1 (2012), no. 1, 1-7. 
  5. J. Cheshmavar, S. K. Hosseini, and C. Park, Some results on n-Jordan homomorphisms, Bull. Korean Math. Soc. 57 (2020), no. 1, 31-35. https://doi.org/10.4134/BKMS.b180719 
  6. M. Eshaghi Gordji, n-Jordan homomorphisms, Bull. Aust. Math. Soc. 80 (2009), no. 1, 159-164. https://doi.org/10.1017/S000497270900032X 
  7. E. Gselmann, On approximate n-Jordan homomorphisms, Ann. Math. Sil. No. 28 (2014), 47-58. 
  8. S. Hejazian, M. Mirzavaziri, and M. S. Moslehian, n-homomorphisms, Bull. Iranian Math. Soc. 31 (2005), no. 1, 13-23, 88. 
  9. I. N. Herstein, Jordan homomorphisms, Trans. Amer. Math. Soc. 81 (1956), 331-341. https://doi.org/10.2307/1992920 
  10. N. Jacobson and C. E. Rickart, Jordan homomorphisms of rings, Trans. Amer. Math. Soc. 69 (1950), 479-502. https://doi.org/10.2307/1990495 
  11. I. Kaplansky, Semi-automorphisms of rings, Duke Math. J. 14 (1947), 521-525. http://projecteuclid.org/euclid.dmj/1077474293  1077474293
  12. Y.-H. Lee, Stability of n-Jordan homomorphisms from a normed algebra to a Banach algebra, Abstr. Appl. Anal. 2013 (2013), Art. ID 691025, 5 pp. https://doi.org/10.1155/2013/691025 
  13. W. Zelazko, ˙ A characterization of multiplicative linear functionals in complex Banach algebras, Studia Math. 30 (1968), 83-85. https://doi.org/10.4064/sm-30-1-83-85 
  14. A. Zivari-Kazempour, A characterisation of 3-Jordan homomorphisms on Banach algebras, Bull. Aust. Math. Soc. 93 (2016), no. 2, 301-306. https://doi.org/10.1017/S0004972715001057 
  15. A. Zivari-Kazempour, Automatic continuity of n-Jordan homomorphisms on Banach algebras, Commun. Korean Math. Soc. 33 (2018), no. 1, 165-170. https://doi.org/10.4134/CKMS.c170071 
  16. A. Zivari-Kazempour, A characterization of Jordan and 5-Jordan homomorphisms between Banach algebras, Asian-Eur. J. Math. 11 (2018), no. 2, 1850021, 10 pp. https://doi.org/10.1142/S1793557118500213 
  17. A. Zivari-Kazempour and M. Valaei, Characterization of n-Jordan homomorphisms on rings, Tamkang J. Math. 53 (2022), no. 1, 89-97. https://doi.org/10.5556/j.tkjm.53.2022.3644