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Start Over Subject extended centroid

1. Derivations with power central values on Lie ideals in prime rings

Creator:
Dhara, Basudeb and Sharma, Rajendra K.
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
prime ring, derivation, extended centroid, and martindale quotient ring
Language:
English
Description:
Let $R$ be a prime ring of char $R\ne 2$ with a nonzero derivation $d$ and let $U$ be its noncentral Lie ideal. If for some fixed integers $n_1\ge 0, n_2\ge 0, n_3\ge 0$, $( u^{n_1}[d(u),u]u^{n_2})^{n_3}\in Z(R)$ for all $u \in U$, then $R$ satisfies $S_4$, the standard identity in four variables.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public

2. Generalized derivations on Lie ideals in prime rings

Creator:
Dhara, Basudeb, Kar, Sukhendu, and Mondal, Sachhidananda
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
prime ring, derivation, generalized derivation, extended centroid, Utumi quotient ring, Lie ideal, and Banach algebra
Language:
English
Description:
Let $R$ be a prime ring with its Utumi ring of quotients $U$ and extended centroid $C$. Suppose that $F$ is a generalized derivation of $R$ and $L$ is a noncentral Lie ideal of $R$ such that $F(u)[F(u),u]^n=0$ for all $u \in L$, where $n\geq 1$ is a fixed integer. Then one of the following holds: \begin {itemize} \item [(1)] there exists $\lambda \in C$ such that $F(x)=\lambda x$ for all $x\in R$; \item [(2)] $R$ satisfies $s_4$ and $F(x)=ax+xb$ for all $x\in R$, with $a, b\in U$ and $a-b\in C$; \item [(3)] $\mathop {\rm char}(R)=2$ and $R$ satisfies $s_4$. \end {itemize} As an application we also obtain some range inclusion results of continuous generalized derivations on Banach algebras.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public