Geodesic
Some properties of Lorenzen ideal systems
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 287-295

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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.
Classification : 06F05, 06F15, 06F20, 18A23
Keywords: $r$-ideal; $r_a$-system; system of finite character 
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     author = {Kalapodi, A. and Kontolatou, A. and Mo\v{c}ko\v{r}, J.},
     title = {Some properties of {Lorenzen} ideal systems},
     journal = {Archivum mathematicum},
     pages = {287--295},
     publisher = {mathdoc},
     volume = {36},
     number = {4},
     year = {2000},
     mrnumber = {1811173},
     zbl = {1047.06011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/ARM_2000__36_4_a5/}
}
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Kalapodi, A.; Kontolatou, A.; Močkoř, J. Some properties of Lorenzen ideal systems. Archivum mathematicum, Tome 36 (2000) no. 4, pp. 287-295. http://geodesic.mathdoc.fr/item/ARM_2000__36_4_a5/