Research Article
BibTex RIS Cite

Year 2022, Volume: 43 Issue: 1, 105 - 112, 30.03.2022

Damla Yılmaz

https://doi.org/10.17776/csj.811057
https://izlik.org/JA22UB32NH

Abstract

References

  • [1] Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957) 1093-1100.
  • [2] Maksa Gy., A remark on symmetric biadditive functions having nonnegative diagonalization, Glasnik. Mat., 15(35) (1980) 279-282.
  • [3] Vukman J., Symmetric biderivations on prime and semiprime rings, Aequa. Math. 38 (1989) 245-254.
  • [4] Vukman J., Two results concerning symmetric biderivations on prime rings, Aequa. Math., 40 (1990) 181-189.
  • [5] Bergen J., Derivations in prime rings, Canadian Math. Bull., 26(3) (1983) 267-270.
  • [6] Chang J. C., On semiderivations of prime rings, Chinese Journal Mathematics, 12(4) (1984) 255-262.
  • [7] Bresar M., Vukman J., Orthogonal derivation and extension of a theorem of Posner, Rad. Mat. 5(2) (1989) 237-246.
  • [8] Reddy C. J. S., Reddy B. R., Orthogonal symmetric bi-derivations in semiprime rings, International Journal of Mathematics and Statistics Studies, 4(1) (2016) 22-29.
  • [9] Yılmaz D., Yazarlı H., (to appear), On symmetric bi-semiderivations of prime rings.

Orthogonal Semiderivations and Symmetric Bi-semiderivations in Semiprime Rings

Year 2022, Volume: 43 Issue: 1, 105 - 112, 30.03.2022

Damla Yılmaz

https://doi.org/10.17776/csj.811057
https://izlik.org/JA22UB32NH

Abstract

In this paper, orthogonality for symmetric bi-semiderivations is defined and some results are obtained when two symmetric bi-semiderivations are orthogonal. Also, this paper gives the notion of orthogonality between semiderivations and symmetric bi-semiderivations of a 2-torsion free semiprime ring and offers some results of orthogonality.In this paper, orthogonality for symmetric bi-semiderivations is defined and some results are obtained when two symmetric bi-semiderivations are orthogonal. Also, this paper gives the notion of orthogonality between semiderivations and symmetric bi-semiderivations of a 2-torsion free semiprime ring and offers some results of orthogonality.

Keywords

Semiderivation Bi-semiderivation Semiprime ring Orthogonal derivation.

References

  • [1] Posner E. C., Derivations in prime rings, Proc. Amer. Math. Soc., 8 (1957) 1093-1100.
  • [2] Maksa Gy., A remark on symmetric biadditive functions having nonnegative diagonalization, Glasnik. Mat., 15(35) (1980) 279-282.
  • [3] Vukman J., Symmetric biderivations on prime and semiprime rings, Aequa. Math. 38 (1989) 245-254.
  • [4] Vukman J., Two results concerning symmetric biderivations on prime rings, Aequa. Math., 40 (1990) 181-189.
  • [5] Bergen J., Derivations in prime rings, Canadian Math. Bull., 26(3) (1983) 267-270.
  • [6] Chang J. C., On semiderivations of prime rings, Chinese Journal Mathematics, 12(4) (1984) 255-262.
  • [7] Bresar M., Vukman J., Orthogonal derivation and extension of a theorem of Posner, Rad. Mat. 5(2) (1989) 237-246.
  • [8] Reddy C. J. S., Reddy B. R., Orthogonal symmetric bi-derivations in semiprime rings, International Journal of Mathematics and Statistics Studies, 4(1) (2016) 22-29.
  • [9] Yılmaz D., Yazarlı H., (to appear), On symmetric bi-semiderivations of prime rings.
There are 9 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Damla Yılmaz 0000-0002-6741-8669

Submission Date October 15, 2020
Acceptance Date March 5, 2022
Publication Date March 30, 2022
DOI https://doi.org/10.17776/csj.811057
IZ https://izlik.org/JA22UB32NH
Published in Issue Year 2022 Volume: 43 Issue: 1

Cite

APA Yılmaz, D. (2022). Orthogonal Semiderivations and Symmetric Bi-semiderivations in Semiprime Rings. Cumhuriyet Science Journal, 43(1), 105-112. https://doi.org/10.17776/csj.811057

Cited By

A Note on the Trace of Generalized Permuting Tri-Derivations
Cumhuriyet Science Journal
https://doi.org/10.17776/csj.1333355

As of 2026, Cumhuriyet Science Journal will be published in six issues per year, released in February, April, June, August, October, and December