Angeliki Kontolatou, Department of Mathematics, University of Patras, 26500 Patras, GREECE
Jiri Mockor, Department of Mathematics, University of Ostrava, CZ-702 00 Ostrava, Brafova 7, CZECH REPUBLIC
E-mail: Kalapodi@math.upatras.gr, angelika@math.upatras.gr, Mockor@osu.cz
Abstract. 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.
AMSclassification. 06F05, 06F20
Keywords. $r$-ideal, $r_a$-system, system of finite character