| Title:
|
Some properties of Lorenzen ideal systems (English) |
| Author:
|
Kalapodi, A. |
| Author:
|
Kontolatou, A. |
| Author:
|
Močkoř, J. |
| Language:
|
English |
| Journal:
|
Archivum Mathematicum |
| ISSN:
|
0044-8753 (print) |
| ISSN:
|
1212-5059 (online) |
| Volume:
|
36 |
| Issue:
|
4 |
| Year:
|
2000 |
| Pages:
|
287-295 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
Let $G$ be a partially ordered abelian group ($po$-group). The construction of the Lorenzen ideal $r_a$-system in $G$ is investigated and the functorial properties of this construction with respect to the semigroup $(R(G),\oplus ,\le )$ of all $r$-ideal systems defined on $G$ are derived, where for $r,s\in R(G)$ and a lower bounded subset $X\subseteq G$, $X_{r\oplus s}=X_r\cap X_s$. It is proved that Lorenzen construction is the natural transformation between two functors from the category of $po$-groups with special morphisms into the category of abelian ordered semigroups. (English) |
| Keyword:
|
$r$-ideal |
| Keyword:
|
$r_a$-system |
| Keyword:
|
system of finite character |
| MSC:
|
06F05 |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
18A23 |
| idZBL:
|
Zbl 1047.06011 |
| idMR:
|
MR1811173 |
| . |
| Date available:
|
2008-06-06T22:26:19Z |
| Last updated:
|
2012-05-10 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/107743 |
| . |
| 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:
|
[6] Kalapodi, A. and Kontolatou, A.: Algebraic and categorical properties of $r$-ideal systems.International Journal of Mathematics and Mathematical Sciences, to appear. |
| Reference:
|
[7] Lorenzen, P.: Abstrakte Begründung der multiplikativen Idealtheorie.Math. Z. 45 (1939), 533–553. Zbl 0021.38703, MR 0000604 |
| Reference:
|
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| Reference:
|
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| Reference:
|
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| . |
