| Title:
|
Generalized derivations on Lie ideals in prime rings (English) |
| Author:
|
Dhara, Basudeb |
| Author:
|
Kar, Sukhendu |
| Author:
|
Mondal, Sachhidananda |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
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1572-9141 (online) |
| Volume:
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65 |
| Issue:
|
1 |
| Year:
|
2015 |
| Pages:
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179-190 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
prime ring |
| Keyword:
|
derivation |
| Keyword:
|
generalized derivation |
| Keyword:
|
extended centroid |
| Keyword:
|
Utumi quotient ring |
| Keyword:
|
Lie ideal |
| Keyword:
|
Banach algebra |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| MSC:
|
16W80 |
| idZBL:
|
Zbl 06433728 |
| idMR:
|
MR3336032 |
| DOI:
|
10.1007/s10587-015-0167-4 |
| . |
| Date available:
|
2015-04-01T12:32:31Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144220 |
| . |
| Reference:
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