| Title:
|
Commutativity of rings with polynomial constraints (English) |
| Author:
|
Khan, Moharram A. |
| Language:
|
English |
| Journal:
|
Czechoslovak Mathematical Journal |
| ISSN:
|
0011-4642 (print) |
| ISSN:
|
1572-9141 (online) |
| Volume:
|
52 |
| Issue:
|
2 |
| Year:
|
2002 |
| Pages:
|
401-413 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $p$, $ q$ and $r$ be fixed non-negative integers. In this note, it is shown that if $R$ is left (right) $s$-unital ring satisfying $[f(x^py^q) - x^ry, x] = 0$ ($[f(x^py^q) - yx^r, x] = 0$, respectively) where $f(\lambda ) \in {\lambda }^2{\mathbb Z}[\lambda ]$, then $R$ is commutative. Moreover, commutativity of $R$ is also obtained under different sets of constraints on integral exponents. Also, we provide some counterexamples which show that the hypotheses are not altogether superfluous. Thus, many well-known commutativity theorems become corollaries of our results. (English) |
| Keyword:
|
automorphism |
| Keyword:
|
commutativity |
| Keyword:
|
local ring |
| Keyword:
|
polynomial identity |
| Keyword:
|
$s$-unital ring |
| MSC:
|
16R50 |
| MSC:
|
16U70 |
| MSC:
|
16U80 |
| MSC:
|
16U99 |
| idZBL:
|
Zbl 1014.16032 |
| idMR:
|
MR1905447 |
| . |
| Date available:
|
2009-09-24T10:52:20Z |
| Last updated:
|
2020-07-03 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/127728 |
| . |
| Reference:
|
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| Reference:
|
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| . |
