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On Generalized Semi-derivations and Jordan Ideals

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Abstract

Let R be a two-torsion free prime ring. In this article, we study the commutativity of the ring with the generalized semi-derivation F that satisfies certain conditions in prime rings and apply our results to \((\sigma ,\tau )\)-Jordan ideals.

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References

  1. Bergen, J.: Derivations in prime rings. Can. Math. Bull. 26, 267–270 (1983)

    Article  MathSciNet  Google Scholar 

  2. Bharathi, M.V.L., Jayalakshmi, K.: Semi-derivations in prime rings. Int. J. Pure Appl. Math. 113–116, 101–109 (2017)

    Google Scholar 

  3. Bresar, M.: On the distance of the composition of two derivations to the generalized derivations. Glasgow Math. 33, 89–93 (1991)

    Article  MathSciNet  Google Scholar 

  4. Chang, J.C.: On semi-derivations of prime rings. Chin. J. Math. 12, 255–262 (1984)

    MATH  Google Scholar 

  5. De Filippis, V., Mamouni, A., Oukhtite, L.: Generalized Jordan semi-derivations in prime rings. Can. Math. Bull. 58–2, 263–270 (2015)

    Article  Google Scholar 

  6. Fırat, A.: Some results for semi derivations of prime rings. Int. J. Pure Appl. Math. 28–3, 363–368 (2006)

    MathSciNet  MATH  Google Scholar 

  7. Güven, E.: On \((\sigma,\tau )\)-left Jordan ideals and generalized derivations. East-West J. Math. 21–1, 58–69 (2019)

    MathSciNet  MATH  Google Scholar 

  8. Güven, E.: On left \((\sigma,\tau )\)-Jordan ideals and generalized derivation. TWMS. J. Appl. Eng. Math. 9–1, 22–29 (2019)

    Google Scholar 

  9. Güven, E., Kaya, K., Soytürk, M.: Some results on \((\sigma,\tau )\)-Lie ideals. Okayama Math. J. 49, 59–64 (2007)

    MathSciNet  MATH  Google Scholar 

  10. Haetinger, C., Mamouni, A.: Semi-derivations and generalized left semi-derivations of prime rings. Palest. J. Math. 7, 28–35 (2018)

    MathSciNet  MATH  Google Scholar 

  11. Kaya, K., Kandamar, H., Aydın, N.: Generalized Jordan structure of prime rings. Doga-Tr. J. Math. 17, 251–258 (1993)

    MathSciNet  MATH  Google Scholar 

  12. Kaya, K., Gölbaşı, Ö., Aydın, N.: Some results for generalized Lie ideals in prime rings with derivation II. Appl. Math. E-Notes 1, 24–30 (2001)

    MathSciNet  MATH  Google Scholar 

  13. Mayne, J.H.: Centralizing mappings of prime rings. Can. Math. Bull. 27, 122–126 (1984)

    Article  MathSciNet  Google Scholar 

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Acknowledgements

The author is thankful to the referee for his/her valuable suggestions. This work has been supported by the Kocaeli University Scientific Research Projects Coordination Unit (ID:1599).

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Correspondence to Evrim Guven.

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Communicated by Ali Taherifar.

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Guven, E. On Generalized Semi-derivations and Jordan Ideals. Bull. Iran. Math. Soc. 48, 2089–2103 (2022). https://doi.org/10.1007/s41980-021-00614-7

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  • DOI: https://doi.org/10.1007/s41980-021-00614-7

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