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Zbl 0842.06013
Conrad, Paul; Martinez, Jorge
On adjoining units to hyper-Archimedean $l$-groups. (English)
[J] Czech. Math. J. 45, No.3, 503-516 (1995). ISSN 0011-4642; ISSN 1572-9141/e

In their earlier paper [Order 7, 183-203 (1990; Zbl 0732.06010)] the authors investigated the notion of complementation of an l-group $G$. In the present paper the definition of simple complementation of $G$ is given (by using the notion of weak unit). Let $G$ be a hyper-archimedean l-group. The main result of the paper is Theorem 6 giving four equivalent conditions for $G$; we quote here two of them: (1) $G$ admits a simple complementation. (2) $G$ can be regarded as a group of real-valued functions on the set $I$ such that (i) $\inf\{g_i : g_i \ne 0\} > 0$, for each $g \in G$, $g \ne 0$; (ii) for each $0 < g \in G$ and each $n \in N$, $g = g_n + g^n$, such that $g_n \wedge g^n = 0$ and $(g_n)_i < n$, for each $i \in I$, while $(g^n)_i \geq n$ whenever $(g^n)_i > 0$.
[J.Jakubík (Košice)]

MSC 2000:: *06F15 Ordered groups
06D05 Structure and representation theory of distributive lattices

Keywords: weak order unit; simple complementation; hyper-archimedean l-group

Citations: Zbl 0732.06010

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