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A Note on the Trace of Generalized Permuting Tri-Derivations

Year 2024, Volume: 45 Issue: 1, 125 - 129, 28.03.2024

Süleyman Zortaş , Hasret Yazarlı

https://doi.org/10.17776/csj.1333355

Abstract

Many researchers have studied permuting tri-derivation and generalized derivation in prime or semi-prime rings, BCK-algebras, lattices, d-algebras, MV-algebras and many algebraic structures. Later, they introduced the concept of generalized permuting tri-derivation by combining the concepts of generalized derivation and permuting tri-derivation. In this article, we have examined the properties of generalized permuting triderivation by adding conditions on their traces in prime or semi-prime rings. In addition, we examined the properties of two permuting triderivation by giving a relation between their traces.

Keywords

Prime ring semiprime ring permuting triderivation generalized permuting triderivation

References

  • [1] Posner, E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957) 1093-1100.
  • [2] Bresar, M., On the distance of the compositions of two derivations to generalized derivations, Glasgow Math. J. 33 (1991) 89-93.
  • [3] Maksa, Gy., A remark on symmetric bi-additive functions having non-negative diagonalization, Glasnik Mat., III. Ser. 15(2) (1980) 279-282.
  • [4] Öztürk, M. A., Permuting tri-derivations in prime and semi-prime rings, East Asian Math. J. 15 (1999) No. 2, 177-190.
  • [5] Durna, H., Symmetric bi-derivation on hyperrings, Cumhuriyet University Faculty of Science Journal, 37 (4) (2016).
  • [6] Yılmaz, D., Orthogonal semiderivations and symmetric bi-semiderivations in semiprime ring, Cumhuriyet Science Journal, 43 (1) (2022).
  • [7] Çeven, Y., Symmetric bi-derivations of lattices, Quaestiones Mathematicae, 32(2009), 241-245.
  • [8] Ilbıra, S., Fırat, A., Jun, Y. B., On symmetric bi-derivations of BCI-algebras, Applied Mathematical Sciences, 60 (5) (2011), 2957-2964.
  • [9] Öztürk, M. A., Yazarli, H., Kim, K. H., Permuting tri-derivations in lattices, Quaestiones Mathematicae, 32 (2009), 415-425.
  • [10] Yılmaz, D., Davvaz, B., Yazarlı, H., Permuting tri-derivations in MV-algebras, Malaya Journal of Matematik, 11 (02) (2022), 142-150.
  • [11] Yazarli, H., Permuting triderivations of prime and semiprime rings, Miskolc Mathematical Notes, 18 (1) (2017) 489-497.
  • [12] Ali, A., Shujat, F., Khan, S., On Commuting Traces of Generalized Biderivations of Prime Rings, Italian Journal of Pure and Applied Mathematics, N. 34 (2015) 123-132.
  • [13] Mayne, J. H., Ideals and centralizing mappings in prime rings, Proc. Amer. Math. Soc., 86 (2) (1982) 211-212

Year 2024, Volume: 45 Issue: 1, 125 - 129, 28.03.2024

Süleyman Zortaş , Hasret Yazarlı

https://doi.org/10.17776/csj.1333355

Abstract

References

  • [1] Posner, E. C., Derivations in prime rings, Proc. Amer. Math. Soc. 8 (1957) 1093-1100.
  • [2] Bresar, M., On the distance of the compositions of two derivations to generalized derivations, Glasgow Math. J. 33 (1991) 89-93.
  • [3] Maksa, Gy., A remark on symmetric bi-additive functions having non-negative diagonalization, Glasnik Mat., III. Ser. 15(2) (1980) 279-282.
  • [4] Öztürk, M. A., Permuting tri-derivations in prime and semi-prime rings, East Asian Math. J. 15 (1999) No. 2, 177-190.
  • [5] Durna, H., Symmetric bi-derivation on hyperrings, Cumhuriyet University Faculty of Science Journal, 37 (4) (2016).
  • [6] Yılmaz, D., Orthogonal semiderivations and symmetric bi-semiderivations in semiprime ring, Cumhuriyet Science Journal, 43 (1) (2022).
  • [7] Çeven, Y., Symmetric bi-derivations of lattices, Quaestiones Mathematicae, 32(2009), 241-245.
  • [8] Ilbıra, S., Fırat, A., Jun, Y. B., On symmetric bi-derivations of BCI-algebras, Applied Mathematical Sciences, 60 (5) (2011), 2957-2964.
  • [9] Öztürk, M. A., Yazarli, H., Kim, K. H., Permuting tri-derivations in lattices, Quaestiones Mathematicae, 32 (2009), 415-425.
  • [10] Yılmaz, D., Davvaz, B., Yazarlı, H., Permuting tri-derivations in MV-algebras, Malaya Journal of Matematik, 11 (02) (2022), 142-150.
  • [11] Yazarli, H., Permuting triderivations of prime and semiprime rings, Miskolc Mathematical Notes, 18 (1) (2017) 489-497.
  • [12] Ali, A., Shujat, F., Khan, S., On Commuting Traces of Generalized Biderivations of Prime Rings, Italian Journal of Pure and Applied Mathematics, N. 34 (2015) 123-132.
  • [13] Mayne, J. H., Ideals and centralizing mappings in prime rings, Proc. Amer. Math. Soc., 86 (2) (1982) 211-212
There are 13 citations in total.

Details

Primary Language English
Subjects Applied Mathematics (Other)
Journal Section Natural Sciences
Authors

Süleyman Zortaş 0000-0002-6079-0695

Hasret Yazarlı 0000-0002-9987-2970

Publication Date March 28, 2024
Submission Date July 26, 2023
Acceptance Date November 17, 2023
Published in Issue Year 2024Volume: 45 Issue: 1

Cite

APA Zortaş, S., & Yazarlı, H. (2024). A Note on the Trace of Generalized Permuting Tri-Derivations. Cumhuriyet Science Journal, 45(1), 125-129. https://doi.org/10.17776/csj.1333355
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