| Title:
|
Automorphisms and generalized skew derivations which are strong commutativity preserving on polynomials in prime and semiprime rings (English) |
| Author:
|
de Filippis, Vincenzo |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
66 |
| Issue:
|
1 |
| Year:
|
2016 |
| Pages:
|
271-292 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a prime ring of characteristic different from 2, $Q_r$ its right Martindale quotient ring and $C$ its extended centroid. Suppose that $F$, $G$ are generalized skew derivations of $R$ with the same associated automorphism $\alpha $, and $p(x_1,\ldots ,x_n)$ is a non-central polynomial over $C$ such that $$ [F(x),\alpha (y)]=G([x,y]) $$ for all $x,y \in \{p(r_1,\ldots ,r_n)\colon r_1,\ldots ,r_n \in R\}$. Then there exists $\lambda \in C$ such that $F(x)=G(x)=\lambda \alpha (x)$ for all $x\in R$. (English) |
| Keyword:
|
generalized skew derivation |
| Keyword:
|
prime ring |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 06587889 |
| idMR:
|
MR3483238 |
| DOI:
|
10.1007/s10587-016-0255-0 |
| . |
| Date available:
|
2016-04-07T15:13:22Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/144888 |
| . |
| Reference:
|
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| . |
