aequationes mathematicae

, Volume 64, Issue 1–2, pp 136–144 | Cite as

Skew-commuting and commuting mappings in rings

  • K.-H. Park
  • Y.-S. Jung


We study some maps which are skew-commuting or skew-centralizing on additive subgroups of rings with a left identity; and we present some results concerning commuting mappings in semiprime rings.¶ The first main part: Let n denote an arbitrary positive integer. Let R be a ring with left identity e, and let H be an additive subgroup of R containing e. Let \( G : R \times R \to R \) be a symmetric bi-additive mapping and let \( g \) be the trace of G. Let R be n!-torsion-free if \( n > 1 \), and 2-torsion-free if n = 1. If \( g \) is n-skew-commuting on H, then \( g(H) = \{0 \} \).¶ The second main part: Let \( n \geq 2 \). If R is an n!-torsion-free semiprime ring, and \( d: R \to R \) is a derivation such that d 2 is n-commuting on R, then d maps R into its center.

Keywords. Skew-commuting maps, commuting maps, derivation. 


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Copyright information

© Birkhäuser Verlag, Basel 2002

Authors and Affiliations

  • K.-H. Park
    • 1
  • Y.-S. Jung
    • 2
  1. 1.Department of Mathematics Education, Seowon University, Chongju, Chungbuk 361-742, Korea,¶ e-mail:
  2. 2.Department of Mathematics, Chungnam National University, Taejon 305-764, Korea,¶ e-mail:

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