An equation related to two-sided centralizers in prime rings

• Autores: Maja Fosner, Joso Vukman
• Localización: Houston journal of mathematics, ISSN 0362-1588, Vol. 35, Nº 2, 2009, págs. 353-361
• Idioma: inglés
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• Resumen

  • In this paper we prove the following result: Let R be a prime ring and let T : R ? R be an additive mapping satisfying the relation nT(xn)=T(x)xn-1 + xT(x)xn-2 + ... + xn-1T(x) for all x in R where n > 1 is some fixed integer. If char(R) = 0 or n = char(R) ? 2, then T is of the form T(x) = ?x for all x in R and some fixed element ? in R where C is the extended centroid of R.