Derivations in semiprime rings and Banach algebras

Journal of Linear and Topological Algebra

مقاله 1، دوره 02، شماره 03، آذر 2013، صفحه 129-135   

نویسندگان

Sh. Sahebi؛ V. Rahmani^*

Department of Mathematics, Islamic Azad University, Central Tehran Branch, P. O. Box 14168-94351, Tehran, Iran

چکیده

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.

کلیدواژه‌ها

prime ring؛ semiprime ring؛ derivation؛ Utumi quotient ring؛ Banach algebra

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