| Title:
|
The nil radical of an Archimedean partially ordered ring with positive squares (English) |
| Author:
|
Lavrič, Boris |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
35 |
| Issue:
|
2 |
| Year:
|
1994 |
| Pages:
|
231-238 |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $R$ be an Archimedean partially ordered ring in which the square of every element is positive, and $N(R)$ the set of all nilpotent elements of $R$. It is shown that $N(R)$ is the unique nil radical of $R$, and that $N(R)$ is locally nilpotent and even nilpotent with exponent at most $3$ when $R$ is 2-torsion-free. $R$ is without non-zero nilpotents if and only if it is 2-torsion-free and has zero annihilator. The results are applied on partially ordered rings in which every element $a$ is expressed as $a=a_1-a_2$ with positive $a_1$, $a_2$ satisfying $a_1a_2=a_2a_1=0$. (English) |
| Keyword:
|
partially ordered ring |
| Keyword:
|
Archimedean |
| Keyword:
|
nil radical |
| Keyword:
|
nilpotent |
| MSC:
|
06F25 |
| MSC:
|
16N40 |
| MSC:
|
16W80 |
| idZBL:
|
Zbl 0805.06017 |
| idMR:
|
MR1286569 |
| . |
| Date available:
|
2009-01-08T18:10:32Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/118661 |
| . |
| 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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| Reference:
|
[9] Szász F.A.: Radicals of Rings.Akademiai Kiado - John Wiley & Sons, Budapest-ChichesterNew York-Brisbane-Toronto, 1981. MR 0636787 |
| . |
