Some properties of Lorenzen ideal systems
Kalapodi, Aleka ; Kontolatou, Angeliki ; Močkoř, Jiří
Archivum Mathematicum, Tome 036 (2000), p. 287-295 / Harvested from Czech Digital Mathematics Library
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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.

Publié le : 2000-01-01
Classification:  06F05,  06F15,  06F20,  18A23 
@article{107743,
     author = {Aleka Kalapodi and Angeliki Kontolatou and Ji\v r\'\i\ Mo\v cko\v r},
     title = {Some properties of Lorenzen ideal systems},
     journal = {Archivum Mathematicum},
     volume = {036},
     year = {2000},
     pages = {287-295},
     zbl = {1047.06011},
     mrnumber = {1811173},
     language = {en},
     url = {http://dml.mathdoc.fr/item/107743}
}

Kalapodi, Aleka; Kontolatou, Angeliki; Močkoř, Jiří. Some properties of Lorenzen ideal systems. Archivum Mathematicum, Tome 036 (2000) pp. 287-295. http://gdmltest.u-ga.fr/item/107743/

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