A note on power values of generalized derivation in prime ring and noncommutative Banach algebras

الموضوعات :

Sh. Sahebi ¹ , V. Rahmani ²

1 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran
2 - Department of Mathematics, Islamic Azad University, Central Tehran Branch, PO. Code 14168-94351, Iran

تاريخ الإرسال : 07 الأحد , صفر, 1433 تاريخ التأكيد : 07 الأحد , صفر, 1433 تاريخ الإصدار : 08 الخميس , ربيع الثاني, 1433

الکلمات المفتاحية: prime ring, Banach algebras, generalized derivation, Martindale quotient ring,

ملخص المقالة :

Let $R$ be a prime ring with extended centroid $C$, $H$ a generalized derivationof $R$ and $n\geq 1$ a fixed integer. In this paper we study the situations: (1) If $(H(xy))^n =(H(x))^n(H(y))^n$ for all $x,y\in R$; (2) obtain some related result in case $R$ is a noncommutativeBanach algebra and $H$ is continuous or spectrally bounded.

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