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IDENTITIES WITH ADDITIVE MAPPINGS IN SEMIPRIME RINGS

  • Fosner, Ajda ;
  • Ur Rehman, Nadeem
  • Received : 2013.02.12
  • Published : 2014.01.31

Abstract

The aim of this paper is to prove the next result. Let n > 1 be an integer and let R be a n!-torsion free semiprime ring. Suppose that f : R ${\rightarrow}$ R is an additive mapping satisfying the relation [f(x), $x^n$] = 0 for all $x{\in}R$. Then f is commuting on R.

Keywords

prime ring;semiprime ring;additive mapping;centralizing mapping;commuting mapping

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Cited by

  1. Remarks on Certain Identities with Derivations on Semiprime Rings vol.66, pp.10, 2015, https://doi.org/10.1007/s11253-015-1037-9
  2. On skew-commuting mappings in semiprime rings vol.66, pp.4, 2016, https://doi.org/10.1515/ms-2015-0183