| Title:
|
Generalized reverse derivations and commutativity of prime rings (English) |
| Author:
|
Huang, Shuliang |
| Language:
|
English |
| Journal:
|
Communications in Mathematics |
| ISSN:
|
1804-1388 (print) |
| ISSN:
|
2336-1298 (online) |
| Volume:
|
27 |
| Issue:
|
1 |
| Year:
|
2019 |
| Pages:
|
43-50 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be a prime ring with center $Z(R)$ and $I$ a nonzero right ideal of $R$. Suppose that $R$ admits a generalized reverse derivation $(F,d)$ such that $d(Z(R))\neq 0$. In the present paper, we shall prove that if one of the following conditions holds: (i) $F(xy)\pm xy\in Z(R)$, (ii) $F([x,y])\pm [F(x),y]\in Z(R)$, (iii) $F([x,y])\pm [F(x),F(y)]\in Z(R)$, (iv) $F(x\circ y)\pm F(x)\circ F(y)\in Z(R)$, (v) $[F(x),y]\pm [x,F(y)]\in Z(R)$, (vi) $F(x)\circ y\pm x\circ F(y)\in Z(R)$ for all $x,y \in I$, then $R$ is commutative. (English) |
| Keyword:
|
Prime rings |
| Keyword:
|
reverse derivations |
| Keyword:
|
generalized reverse derivations. |
| MSC:
|
16A70 |
| MSC:
|
16N60 |
| MSC:
|
16W25 |
| idZBL:
|
Zbl 07368958 |
| idMR:
|
MR3977476 |
| . |
| Date available:
|
2019-06-28T14:48:40Z |
| Last updated:
|
2021-11-01 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/147767 |
| . |
| Reference:
|
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| Reference:
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| . |
