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Start Over Subject generalized derivation

1. Generalized derivations associated with Hochschild 2-cocycles on some algebras

Creator:
Li, Jiankui and Zhou, Jiren
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
CSL algebra, generalized derivation, generalized Jordan derivation, and Hochschild 2-cocycle
Language:
English
Description:
We investigate a new type of generalized derivations associated with Hochschild 2-cocycles which was introduced by A. Nakajima. We show that every generalized Jordan derivation of this type from CSL algebras or von Neumann algebras into themselves is a generalized derivation under some reasonable conditions. We also study generalized derivable mappings at zero point associated with Hochschild 2-cocycles on CSL algebras.
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

3. Generalized Jordan derivations associated with Hochschild 2-cocycles of triangular algebras

Creator:
Majieed, Asia and Zhou, Jiren
Format:
bez média and svazek
Type:
model:article and TEXT
Subject:
generalized Jordan derivation, generalized derivation, Hochschild 2-cocycle, and triangular algebra
Language:
English
Description:
In this paper, we investigate a new type of generalized derivations associated with Hochschild 2-cocycles which is introduced by A.Nakajima (Turk.\ J.\ Math.\ 30 (2006), 403--411). We show that if $\mathcal U$ is a triangular algebra, then every generalized Jordan derivation of above type from $\mathcal U$ into itself is a generalized derivation.
Rights:
http://creativecommons.org/publicdomain/mark/1.0/ and policy:public