| Title:
|
Derivations with Engel conditions in prime and semiprime rings (English) |
| Author:
|
Huang, Shuliang |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
61 |
| Issue:
|
4 |
| Year:
|
2011 |
| Pages:
|
1135-1140 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a prime ring, $I$ a nonzero ideal of $R$, $d$ a derivation of $R$ and $m, n$ fixed positive integers. (i) If $(d[x,y])^{m}=[x,y]_{n}$ for all $x,y\in I$, then $R$ is commutative. (ii) If $\mathop {\rm Char}R\neq 2$ and $[d(x),d(y)]_{m}=[x,y]^{n}$ for all $x,y\in I$, then $R$ is commutative. Moreover, we also examine the case when $R$ is a semiprime ring. (English) |
| Keyword:
|
prime and semiprime rings |
| Keyword:
|
ideal |
| Keyword:
|
derivation |
| Keyword:
|
GPIs |
| MSC:
|
16N60 |
| MSC:
|
16R50 |
| MSC:
|
16U70 |
| MSC:
|
16U80 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 1240.16048 |
| idMR:
|
MR2886261 |
| DOI:
|
10.1007/s10587-011-0053-7 |
| . |
| Date available:
|
2011-12-16T15:54:33Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/141811 |
| . |
| Reference:
|
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