DOI QR코드

DOI QR Code

GENERALIZED DERIVATIONS IN RING WITH INVOLUTION INVOLVING SYMMETRIC AND SKEW SYMMETRIC ELEMENTS

  • Souad Dakir (Department of Mathematics Faculty of Sciences University Moulay Ismail) ;
  • Hajar El Mir (Department of Mathematics Faculty of Science and Technology, University S. M. Ben Abdellah) ;
  • Abdellah Mamouni (Department of Mathematics Faculty of Sciences University Moulay Ismail)
  • 투고 : 2023.03.08
  • 심사 : 2023.09.13
  • 발행 : 2024.01.31

초록

In this paper we will demonstrate some results on a prime ring with involution by introducing two generalized derivations acting on symmetric and skew symmetric elements. This approach allows us to generalize some well known results. Furthermore, we provide examples to show that various restrictions imposed in the hypotheses of our theorems are not superfluous.

키워드

참고문헌

  1. S. Ali and N. A. Dar, On ∗-centralizing mappings in rings with involution, Georgian Math. J. 21 (2014), no. 1, 25-28. https://doi.org/10.1515/gmj-2014-0006
  2. S. Ali, N. A. Dar, and A. N. Khan, On strong commutativity preserving like maps in rings with involution, Miskolc Math. Notes 16 (2015), no. 1, 17-24. https://doi.org/10.18514/mmn.2015.1297
  3. H. E. Bell and M. N. Daif, On commutativity and strong commutativity-preserving maps, Canad. Math. Bull. 37 (1994), no. 4, 443-447. https://doi.org/10.4153/CMB-1994-064-x
  4. M. Bresar and C. R. Miers, Strong commutativity preserving maps of semiprime rings, Canad. Math. Bull. 37 (1994), no. 4, 457-460. https://doi.org/10.4153/CMB-1994-066-4
  5. C.-L. Chuang, GPIs having coefficients in Utumi quotient rings, Proc. Amer. Math. Soc. 103 (1988), no. 3, 723-728. https://doi.org/10.2307/2046841
  6. N. A. Dar, S. Ali, A. Abbasi, and M. Ayedh, Some commutativity criteria for prime rings with involution involving symmetric and skew symmetric elements, Ukrainskyi Matematychnyi Zhurnal 75 (2023), no. 4, 455-466. https://doi.org/10.37863/umzh.v75i4.6751
  7. N. A. Dar and A. N. Khan, Generalized derivations in rings with involution, Algebra Colloq. 24 (2017), no. 3, 393-399. https://doi.org/10.1142/S1005386717000244
  8. B. Hvala, Generalized derivations in rings, Comm. Algebra 26 (1998), no. 4, 1147-1166. https://doi.org/10.1080/00927879808826190
  9. M. A. Idrissi and L. Oukhtite, Structure of a quotient ring R/P with generalized derivations acting on the prime ideal P and some applications, Indian J. Pure Appl. Math. 53 (2022), no. 3, 792-800. https://doi.org/10.1007/s13226-021-00173-x
  10. T.-K. Lee, Generalized derivations of left faithful rings, Comm. Algebra 27 (1999), no. 8, 4057-4073. https://doi.org/10.1080/00927879908826682
  11. P.-H. Lee and T.-K. Lee, Lie ideals of prime rings with derivations, Bull. Inst. Math. Acad. Sinica 11 (1983), no. 1, 75-80.
  12. J. Ma, X. W. Xu, and F. W. Niu, Strong commutativity-preserving generalized derivations on semiprime rings, Acta Math. Sin. (Engl. Ser.) 24 (2008), no. 11, 1835-1842. https://doi.org/10.1007/s10114-008-7445-0
  13. L. Oukhtite and A. Mamouni, Generalized derivations centralizing on Jordan ideals of rings with involution, Turkish J. Math. 38 (2014), no. 2, 225-232. https://doi.org/10.3906/mat-1203-14
  14. L. Oukhtite, A. Mamouni, and M. Ashraf, Commutativity theorems for rings with differential identities on Jordan ideals, Comment. Math. Univ. Carolin. 54 (2013), no. 4, 447-457.
  15. P. Semrl, Commutativity preserving maps, Linear Algebra Appl. 429 (2008), no. 5-6, 1051-1070. https://doi.org/10.1016/j.laa.2007.05.006