ON (α,β)-SKEW-COMMUTING AND (α,β)-SKEW-CENTRALIZING MAPS IN RINGS WITH LEFT IDENTITY

- Journal title : Communications of the Korean Mathematical Society
- Volume 20, Issue 1, 2005, pp.23-34
- Publisher : The Korean Mathematical Society
- DOI : 10.4134/CKMS.2005.20.1.023

Title & Authors

ON (α,β)-SKEW-COMMUTING AND (α,β)-SKEW-CENTRALIZING MAPS IN RINGS WITH LEFT IDENTITY

JUNG, YONG-SOO; CHANG, ICK-SOON;

JUNG, YONG-SOO; CHANG, ICK-SOON;

Abstract

Let R be a ring with left identity. Let G : be a symmetric biadditive mapping and g the trace of G. Let be an endomorphism and an epimorphism. In this paper we show the following: (i) Let R be 2-torsion-free. If g is ()-skew-commuting on R, then we have G = 0. (ii) If g is ()-skew-centralizing on R, then g is ()-commuting on R. (iii) Let . Let R be (n+1)!-torsion-free. If g is n-()-skew-commuting on R, then we have G = 0. (iv) Let R be 6-torsion-free. If g is 2-()-commuting on R, then g is ()-commuting on R.

Keywords

rings with left identity;

Language

English

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References