This article is cited in 14 papers

On $\tau$-centralizers of semiprime rings

E. Albaş

Ege University

Abstract: Let $R$ be a semiprime 2-torsion free ring, and let $\tau$ be an endomorphism of $R$. Under some conditions we prove that a left Jordan $\tau$-centralizer of $R$ is a left $\tau$-centralizer of $R$. Under the same conditions we also prove that a Jordan $\tau$-centralizer of $R$ is a $\tau$-centralizer of $R$. We thus generalize Zalar's results to the case of $\tau$-centralizers of $R$.

Keywords: prime ring, semiprime ring, left centralizer, left Jordan centralizer, left $\tau$-centralizer, left Jordan $\tau$-centralizer, generalized $(\sigma,\tau)$-derivation, generalized Jordan $(\sigma,\tau)$-derivation.

UDC: 512.5

Received: 31.08.2005

 English version: Siberian Mathematical Journal, 2007, 48:2, 191–196

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