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A Note on Skew-commuting Automorphisms in Prime Rings

ur Rehman, Nadeem;Bano, Tarannum

  • Received : 2014.02.15
  • Accepted : 2014.04.22
  • Published : 2015.03.23

Abstract

Let R be a prime ring with center Z, I a nonzero ideal of R, and ${\sigma}$ a non-trivial automorphism of R such that $\{(x{\circ}y)^{\sigma}-(x{\circ}y)\}^n{\in}Z$ for all $x,y{\in}I$. If either char(R) > n or char (R) = 0, then R satisfies $s_4$, the standard identity in 4 variables.

Keywords

Prime ring;Ideal;Automorphism

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Cited by

  1. Some identities on automorphisms in prime rings 2016, https://doi.org/10.1007/s12215-016-0260-z
  2. -commuting mappings on (semi)-prime rings with applications pp.1532-4125, 2019, https://doi.org/10.1080/00927872.2018.1536203