On n-Jordan derivations in the sense of Herstein

On n-Jordan derivations in the sense of Herstein

We prove that every n -Jordan derivation in the sense of Herstein (Bull Am Math Soc 67:517–531, 1961, p. 528) on n !-torsion free unital commutative rings is a derivation. Furthermore, we prove that every continuous n -Jordan derivation on semiprime normed algebras is a derivation. The results of th...

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Veröffentlicht in:Revista de la Real Academia de Ciencias Exactas, Físicas y Naturales. Serie A, Matemáticas Físicas y Naturales. Serie A, Matemáticas, 2023-04, Vol.117 (2), Article 85
Hauptverfasser: Rostami, Mehdi, Alinejad, Ahmad, Khodaei, Hamid
Format: Artikel
Sprache:eng
Schlagworte:
Applications of Mathematics
Derivation
Mathematical and Computational Physics
Mathematics
Mathematics and Statistics
Original Paper
Rings (mathematics)
Theoretical
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Zusammenfassung:We prove that every n -Jordan derivation in the sense of Herstein (Bull Am Math Soc 67:517–531, 1961, p. 528) on n !-torsion free unital commutative rings is a derivation. Furthermore, we prove that every continuous n -Jordan derivation on semiprime normed algebras is a derivation. The results of this paper improve and generalize the main results of Bridges and Bergen (Proc Am Math Soc 90:25–29, 1984), but under weaker assumptions. Some applications and examples of our results are also provided.
ISSN:1578-7303
1579-1505
DOI:10.1007/s13398-023-01419-5