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On derivations and commuting like elements in prime rings

Lahcen Oukhtite|Omar Ait Zemzami|Jihad Benzaid
장전수학회 (Jangjeon Mathematical Society)|2024.04|Proceedings of the Jangjeon Mathematical Society(장전수학회 논문집) (Proceedings of the Jangjeon Mathematical Society)|제27권 제2호|pp. 219-228|DOI 10.17777/pjms.2024.27.2.011

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참고문헌

키워드

Prime ringsCenter of ringsDerivationsCommutativity
주제분류수학

초록

The purpose of this paper is to investigate some central differential identities involving a fixed element of R, more precisely, we will prove that, if a is a fixed element of R satisfying some special differential identities then a is central. Moreover, the classifications of the involved derivations are also provided.

Abstract

The purpose of this paper is to investigate some central differential identities involving a fixed element of R, more precisely, we will prove that, if a is a fixed element of R satisfying some special differential identities then a is central. Moreover, the classifications of the involved derivations are also provided.

참고문헌 (13)

  1. O. Ait Zemzami, "Commuting-like elements in prime rings with derivations", Rend. Circ. Mat. Palermo, 71(2), pp.665~676 (2022)
  2. N. Aydin, "A note on generalized derivations of prime rings", J. Algebra, 5(1), pp.17~23 (2011)
  3. M. Bresar, "Centralizing mapping and derivation in prime rings", J. Algebra, 156, pp.385~394 (1993)
  4. M. Chacron, "A commutativity theorem for rings", Proc. Amer. Math. Soc, 59(2), pp.211~216 (1976)
  5. C. Haetinger, "Generalized semi-derivations and generalized left semi-derivations of prime rings", Palest. J. Math, 7(I), pp.28~35 (2018)
  6. I. N. Herstein, "On the hypercenter of a ring", J. Algebra, 36(1), pp.509~511 (1975)
  7. I. N. Herstein, "Rings with involution, Chicago Lectures in Mathematics" (1976), The University of Chicago Press
  8. I. N. Herstein, "A note on derivations", Canad. Math. Bull, 21(3), pp.369~370 (1978)
  9. I. N. Herstein, "A note on derivations II", Canad. Math. Bull, 22(4), pp.509~511 (1979)
  10. M. A. Idrissi, "Center-like subsets in rings with deriva-tions or endomorphisms", Commun. Algebra, 47(9), pp.3794~3799 (2019)
  11. M. A. Idrissi, "On derivations of prime rings", Chin. J. Math, 9(2), pp.107~110 (1981)
  12. E. C. Posner, "Derivations in prime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)
  13. J. Vukman, "Centralizers on semprime rings", Proc. Amer. Math. Soc, 8, pp.1093~1100 (1957)

관련 논문AI추천

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