| Title:
|
Classification of rings satisfying some constraints on subsets (English) |
| Author:
|
Khan, Moharram A. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
43 |
| Issue:
|
1 |
| Year:
|
2007 |
| Pages:
|
19-29 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an associative ring with identity $1$ and $J(R)$ the Jacobson radical of $R$. Suppose that $m\ge 1$ is a fixed positive integer and $R$ an $m$-torsion-free ring with $1$. In the present paper, it is shown that $R$ is commutative if $R$ satisfies both the conditions (i) $[x^m,y^m]=0$ for all $x,y\in R\backslash J(R)$ and (ii) $[x,[x,y^m]]=0$, for all $x,y\in R\backslash J(R)$. This result is also valid if (ii) is replaced by (ii)’ $[(yx)^mx^m-x^m(xy)^m,x]=0$, for all $x,y\in R\backslash N(R)$. Our results generalize many well-known commutativity theorems (cf. [1], [2], [3], [4], [5], [6], [9], [10], [11] and [14]). (English) |
| Keyword:
|
Jacobson radical |
| Keyword:
|
nil commutator |
| Keyword:
|
periodic ring |
| MSC:
|
16U80 |
| idZBL:
|
Zbl 1156.16304 |
| idMR:
|
MR2310121 |
| . |
| Date available:
|
2008-06-06T22:50:21Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/108046 |
| . |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| Reference:
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| Reference:
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| . |
