| Title:
|
Commutativity of associative rings through a Streb's classification (English) |
| Author:
|
Ashraf, Mohammad |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
33 |
| Issue:
|
3 |
| Year:
|
1997 |
| Pages:
|
315-321 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $m \geq 0, ~r \geq 0, ~s \geq 0, ~q \geq 0$ be fixed integers. Suppose that $R$ is an associative ring with unity $1$ in which for each $x,y \in R$
there exist polynomials $f(X) \in X^{2} \mbox{$Z \hspace{-2.2mm} Z$}[X], ~g(X), ~h(X) \in X \mbox{$Z \hspace{-2.2mm} Z$}[X]$ such that $\{ 1-g (yx^{m}) \} [x, ~x^{r}y ~-~ x^{s}f (y x^{m}) x^{q}] \{ 1-h(yx^{m}) \} ~=~ 0$. Then $R$ is commutative. Further, result is extended to the case when the integral exponents in the above property depend on the choice of $x$ and $y$. Finally, commutativity of one sided s-unital ring is also obtained when $R$ satisfies some related ring properties. (English) |
| Keyword:
|
factorsubring |
| Keyword:
|
s-unital ring |
| Keyword:
|
commutativity |
| Keyword:
|
commutator |
| Keyword:
|
associative ring |
| MSC:
|
16U70 |
| MSC:
|
16U80 |
| idZBL:
|
Zbl 0913.16017 |
| idMR:
|
MR1601337 |
| . |
| Date available:
|
2008-06-06T21:34:22Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107620 |
| . |
| 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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| Reference:
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| Reference:
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| Reference:
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| . |
