Research Article
BibTex RIS Cite

On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings

Year 2022, Issue: 39, 42 - 53, 30.06.2022

Handan Karahan Neşet Aydın , Didem Yeşil

https://doi.org/10.53570/jnt.1126644
https://izlik.org/JA77TH39KM

Abstract

The algebraic properties and identities of a semiprime ring are investigated with the help of the multiplicative (generalised)-(α, α)-reverse derivation on the non-empty ideal of the semiprime ring.

Keywords

Derivation Reverse Derivation Generalised Derivation Generalised Reverse Derivation

References

  • I. N. Herstein, Jordan Derivations of Prime Rings, Proceedings of the American Mathematical Society 8 (6) (1957) 1104–1110.
  • M. S. Samman, and N. Alyamani, Derivations and Reverse Derivations in Semiprime Rings, International Mathematical Forum 2 (39) (2007) 1895–1902.
  • A. Asma, and A. Bano, Multiplicative (Generalized) Reverse Derivations on Semiprime Ring, European Journal of Pure and Applied Mathematics 11 (3) (2018) 717–729.
  • G. S. Gurninder, and D. Kumar, Annihilator Conditions of Multiplicative Reverse Derivation on Prime Rings, International Electronic Journal of Algebra 25 (2019) 87–103.
  • S. K. Tiwari, R. K. Sharma, and B. Dhara, Some theorems of commutativity on semiprime rings with mappings, Southeast Asian Bulletin of Mathematics 42 (2) (2018) 279–292.
  • Z. S. M. Alhaidary, and A. H. Majeed, Commutativity Results for Multiplicative (Generalized) (α, β)-Reverse Derivations on Prime Rings, Iraqi Journal of Science 62 (9) (2021) 3102–3113.
  • Z. S. M. Alhaidary, and A. H. Majeed, Square Closed Lie Ideals and Multiplicative (Generalised) (α, β)-Reverse Derivation of Prime Rings, Journal of Discrete Mathematical Sciences & Cryptography 24 (7) (2021) 2037–2046.
  • E. Ulutaş, and ¨ O. Gölbaşı, Results on Multiplicative Generalized (α, α)-Derivations, International Journal of Open Problems in Computer Science & Mathematics 13 (3) (2020) 128–135.
  • S. Türkmen, and N. Aydın, Generalized *-Lie ideal of *-Prime Ring, Turkish Journal of Mathematics 41 (4) (2017) 841–853.
  • N. Aydın, E. Koç, and ¨O Gölbaşı, On *-(σ, τ)-Lie Ideals of *-Prime Rings with Derivation, Hacettepe Journal of Mathematics and Statics 47 (5) (2018) 1240–1247.
  • B. Albayrak, and N. Aydın, Reverse and Jordan-biderivation on Prime and semiprime Rings, Adıyaman University Journal of Science 9 (1) (2019) 149–164.
  • B. Albayrak, and D. Yeşil, A Generalized Study on Closed Lie ˙Ideals with (α, α)-derivations, Eskişehir Technical University Journal of Science and Technology B - Theoretical Sciences 7 (2) (2019) 195–203.
  • B. Albayrak, and D. Yeşil, Closed Lie Ideals of Prime Rings with Generalized α-Derivations, International Journal of Mathematics Trends and Technology 65 (7) (2019) 101–109.

Year 2022, Issue: 39, 42 - 53, 30.06.2022

Handan Karahan Neşet Aydın , Didem Yeşil

https://doi.org/10.53570/jnt.1126644
https://izlik.org/JA77TH39KM

Abstract

References

  • I. N. Herstein, Jordan Derivations of Prime Rings, Proceedings of the American Mathematical Society 8 (6) (1957) 1104–1110.
  • M. S. Samman, and N. Alyamani, Derivations and Reverse Derivations in Semiprime Rings, International Mathematical Forum 2 (39) (2007) 1895–1902.
  • A. Asma, and A. Bano, Multiplicative (Generalized) Reverse Derivations on Semiprime Ring, European Journal of Pure and Applied Mathematics 11 (3) (2018) 717–729.
  • G. S. Gurninder, and D. Kumar, Annihilator Conditions of Multiplicative Reverse Derivation on Prime Rings, International Electronic Journal of Algebra 25 (2019) 87–103.
  • S. K. Tiwari, R. K. Sharma, and B. Dhara, Some theorems of commutativity on semiprime rings with mappings, Southeast Asian Bulletin of Mathematics 42 (2) (2018) 279–292.
  • Z. S. M. Alhaidary, and A. H. Majeed, Commutativity Results for Multiplicative (Generalized) (α, β)-Reverse Derivations on Prime Rings, Iraqi Journal of Science 62 (9) (2021) 3102–3113.
  • Z. S. M. Alhaidary, and A. H. Majeed, Square Closed Lie Ideals and Multiplicative (Generalised) (α, β)-Reverse Derivation of Prime Rings, Journal of Discrete Mathematical Sciences & Cryptography 24 (7) (2021) 2037–2046.
  • E. Ulutaş, and ¨ O. Gölbaşı, Results on Multiplicative Generalized (α, α)-Derivations, International Journal of Open Problems in Computer Science & Mathematics 13 (3) (2020) 128–135.
  • S. Türkmen, and N. Aydın, Generalized *-Lie ideal of *-Prime Ring, Turkish Journal of Mathematics 41 (4) (2017) 841–853.
  • N. Aydın, E. Koç, and ¨O Gölbaşı, On *-(σ, τ)-Lie Ideals of *-Prime Rings with Derivation, Hacettepe Journal of Mathematics and Statics 47 (5) (2018) 1240–1247.
  • B. Albayrak, and N. Aydın, Reverse and Jordan-biderivation on Prime and semiprime Rings, Adıyaman University Journal of Science 9 (1) (2019) 149–164.
  • B. Albayrak, and D. Yeşil, A Generalized Study on Closed Lie ˙Ideals with (α, α)-derivations, Eskişehir Technical University Journal of Science and Technology B - Theoretical Sciences 7 (2) (2019) 195–203.
  • B. Albayrak, and D. Yeşil, Closed Lie Ideals of Prime Rings with Generalized α-Derivations, International Journal of Mathematics Trends and Technology 65 (7) (2019) 101–109.
There are 13 citations in total.

Details

Primary Language English
Subjects Mathematical Sciences
Journal Section Research Article
Authors

Handan Karahan This is me 0000-0002-9954-2269

Neşet Aydın 0000-0002-7193-3399

Didem Yeşil 0000-0003-0666-9410

Submission Date June 6, 2022
Publication Date June 30, 2022
DOI https://doi.org/10.53570/jnt.1126644
IZ https://izlik.org/JA77TH39KM
Published in Issue Year 2022 Issue: 39

Cite

APA Karahan, H., Aydın, N., & Yeşil, D. (2022). On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings. Journal of New Theory, 39, 42-53. https://doi.org/10.53570/jnt.1126644
AMA 1.Karahan H, Aydın N, Yeşil D. On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings. JNT. 2022;(39):42-53. doi:10.53570/jnt.1126644
Chicago Karahan, Handan, Neşet Aydın, and Didem Yeşil. 2022. “On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings”. Journal of New Theory, nos. 39: 42-53. https://doi.org/10.53570/jnt.1126644.
EndNote Karahan H, Aydın N, Yeşil D (June 1, 2022) On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings. Journal of New Theory 39 42–53.
IEEE [1]H. Karahan, N. Aydın, and D. Yeşil, “On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings”, JNT, no. 39, pp. 42–53, June 2022, doi: 10.53570/jnt.1126644.
ISNAD Karahan, Handan - Aydın, Neşet - Yeşil, Didem. “On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings”. Journal of New Theory. 39 (June 1, 2022): 42-53. https://doi.org/10.53570/jnt.1126644.
JAMA 1.Karahan H, Aydın N, Yeşil D. On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings. JNT. 2022;:42–53.
MLA Karahan, Handan, et al. “On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings”. Journal of New Theory, no. 39, June 2022, pp. 42-53, doi:10.53570/jnt.1126644.
Vancouver 1.Handan Karahan, Neşet Aydın, Didem Yeşil. On the Multiplicative (Generalised) (α, α)−Derivations of Semiprime Rings. JNT. 2022 Jun. 1;(39):42-53. doi:10.53570/jnt.1126644

Cited By

A New Perspective on $k$-Ideals of a Semiring via Soft Intersection Ideals
Journal of New Theory
https://doi.org/10.53570/jnt.1145507


TR Dizin 26024

Electronic Journals Library 13651

                                EBSCO 36309                                     

DOAJ 33468

Scilit 20865


                                                        SOBİAD 30256


29324 JNT is licensed under a Creative Commons Attribution-NonCommercial 4.0 International Licence (CC BY-NC).

The Journal of New Theory's website content and procedures are publicly accessible under the CC BY-NC license; commercial use requires our permission.