Kyungpook Mathematical Journal

  • 제62권1호
  • /
  • Pages.43-55
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  • 2022
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  • 1225-6951(pISSN)
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  • 0454-8124(eISSN)
경북대학교 자연과학대학 수학과 (Department of Mathematics, Kyungpook National University)
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On n-skew Lie Products on Prime Rings with Involution

  • 투고 : 2021.07.07
  • 심사 : 2021.10.07
  • 발행 : 2022.03.31
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초록

Let R be a *-ring and n ≥ 1 be an integer. The objective of this paper is to introduce the notion of n-skew centralizing maps on *-rings, and investigate the impact of these maps. In particular, we describe the structure of prime rings with involution '*' such that *[x, d(x)]n ∈ Z(R) for all x ∈ R (for n = 1, 2), where d : R → R is a nonzero derivation of R. Among other related results, we also provide two examples to prove that the assumed restrictions on our main results are not superfluous.

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과제정보

The authors are greatful to the learned referee for carefully reading the manuscript. The valuable suggestions have simplified and clarified the paper greatly.

참고문헌

  1. S. Ali and N. A. Dar, On *-centralizing mappings in rings with involution, Georgain Math. J., 21(1)(2014), 25-28. https://doi.org/10.1515/gmj-2014-0006
  2. I. N. Herstein, Ring with Involution, University of Chicago Press, Chicago, 1976.
  3. J. Hou and W. Wang, Strong 2-skew commutativity preserving maps on prime rings with involution, Bull. Malays. Math. Sci. Soc., 42(1)(2019), 33-49. https://doi.org/10.1007/s40840-017-0465-0
  4. E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., 8(1957), 1093-1100. https://doi.org/10.1090/S0002-9939-1957-0095863-0
  5. X. Qi and Y. Zhang, k-skew Lie products on prime rings with involution, Comm. Algebra, 46(3)(2018), 1001-1010. https://doi.org/10.1080/00927872.2017.1335744