Derivations in semiprime rings and Banach algebras

محورهای موضوعی : Rings theory

Sh. Sahebi ¹ (Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 14168-94351, Tehran, Iran)
V. Rahmani ² (Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 14168-94351, Tehran, Iran)

تاریخ دریافت : 1391/10/12 تاریخ پذیرش : 1391/10/12 تاریخ انتشار : 1392/06/10

کلید واژه: prime ring, semiprime ring, derivation, Utumi quotient ring, Banach algebra,

چکیده مقاله :

Let $R$ be a 2-torsion free semiprime ring with extended centroid $C$, $U$ the Utumi quotient ring of $R$ and $m,n>0$ are fixed integers. We show that if $R$ admits derivation $d$ such that $b[[d(x), x]_n,[y,d(y)]_m]=0$ for all $x,y\in R$ where $0\neq b\in R$, then there exists a central idempotent element $e$ of $U$ such that $eU$ is commutative ring and $d$ induce a zero derivation on $(1-e)U$. We also obtain some related result in case $R$ is a non-commutative Banach algebra and d continuous or spectrally bounded.

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