On Symmetric Higher (U, R)-n-Derivation of Prime Rings
Keywords:
Prime ring, derivation, n-derivation, (U,R) derivation, Higher derivation.
Abstract
The main aim of this paper is to define the notions of Symmetric higher (U,R)-n-derivation, (U,R) n-derivation, Jordan(U,R)-n-derivation and higher n-derivation of prime ring to generalize Awtar’s theorem of derivation on Lie ideal of prime ring to symmetric higher(U,R)-n-derivation.
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References
[1]I.N. Herstein, "Topics in Ring Theory", the University of Chicago Press, Chicago, 1969.
[2] K. H. Kim, and Y. H. Lee, "A Note on ∗-Derivation of Prime ∗-Rings", International Mathematical Forum, 12(2017), No. 8, 391-398.
[3] E. C. Posner, "Derivations in Prime Rings", proc. Amer. Math. Soc., 8(1957), 1093 – 1100
[10] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90 (1) (1984), 9-14..
[4] Ashraf, M. and Rehman, N. 2000. On Lie ideals and Jordan left derivations of prime rings, Archivum Mathematicum (Brno) Tomus. 36: 201-206.
[5] Awtar, R. 1988. Jordan derivations and Jordan homomorphisms on prime rings of characteristics 2, Acta Mathemetica Hungarica. 51: 61-63.
[6] Park, K. 2010. Jordan higher left derivations and commutativity in prime rings, Journal of the Chungcheong Mathematical Society. 23(4): 741-748.
[7] Ferro, M. and Haetinger,C. 2002. Higher derivations and a theorem by Herstien, Quaestions Mathematica. 25: 1-9.
[8] Haetinger, C. 2002. Higher derivations on Lie ideals, Tendencias em Mathematica aplicada Computational. 3(1):141-145.
[9] Faraj, A.K., Hatinger, C. and Majeed, A. H. 2010. Generalized higher ) ,( R U - derivations, JP Journal of Algebra, Number Theory and Applications. 16(2): 119-142.
[10] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90 (1) (1984), 9-14.
[11] K. H. Park, "On Prime and Semiprime Rings with Symmetric n-Derivations", J.Chungcheong Math. Soc., 22(2009), No. 3, 451-458.
[12] J. Berger, I. N. Herstein and J. W. Kerr. Lie ideals ana derivations of prime rings, J. Algebra 71 (1981), 259-267.
[2] K. H. Kim, and Y. H. Lee, "A Note on ∗-Derivation of Prime ∗-Rings", International Mathematical Forum, 12(2017), No. 8, 391-398.
[3] E. C. Posner, "Derivations in Prime Rings", proc. Amer. Math. Soc., 8(1957), 1093 – 1100
[10] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90 (1) (1984), 9-14..
[4] Ashraf, M. and Rehman, N. 2000. On Lie ideals and Jordan left derivations of prime rings, Archivum Mathematicum (Brno) Tomus. 36: 201-206.
[5] Awtar, R. 1988. Jordan derivations and Jordan homomorphisms on prime rings of characteristics 2, Acta Mathemetica Hungarica. 51: 61-63.
[6] Park, K. 2010. Jordan higher left derivations and commutativity in prime rings, Journal of the Chungcheong Mathematical Society. 23(4): 741-748.
[7] Ferro, M. and Haetinger,C. 2002. Higher derivations and a theorem by Herstien, Quaestions Mathematica. 25: 1-9.
[8] Haetinger, C. 2002. Higher derivations on Lie ideals, Tendencias em Mathematica aplicada Computational. 3(1):141-145.
[9] Faraj, A.K., Hatinger, C. and Majeed, A. H. 2010. Generalized higher ) ,( R U - derivations, JP Journal of Algebra, Number Theory and Applications. 16(2): 119-142.
[10] R. Awtar, Lie ideals and Jordan derivations of prime rings, Proc. Amer. Math. Soc., 90 (1) (1984), 9-14.
[11] K. H. Park, "On Prime and Semiprime Rings with Symmetric n-Derivations", J.Chungcheong Math. Soc., 22(2009), No. 3, 451-458.
[12] J. Berger, I. N. Herstein and J. W. Kerr. Lie ideals ana derivations of prime rings, J. Algebra 71 (1981), 259-267.
Published
2020-03-31
How to Cite
Khaleel Faraj, A., & Hadi, M. (2020). On Symmetric Higher (U, R)-n-Derivation of Prime Rings . Al-Qadisiyah Journal of Pure Science, 25(2), Math.40-50. Retrieved from https://journalsc.qu.edu.iq/index.php/JOPS/article/view/1056
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Section
Mathematics
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