Geodesic
Some properties of Lorenzen ideal systems
Archivum mathematicum, Tome 36 (2000) no. 4, pp. 287-295 Cet article a éte moissonné depuis la source 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.
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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}
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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/

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