1. On the distributive radical of an Archimedean lattice-ordered group
- Creator:
- Jakubík, Ján
- Format:
- bez média and svazek
- Type:
- model:article and TEXT
- Subject:
- Archimedean $\ell $-group, divisible hull, distributive radical, and complete distributivity
- Language:
- English
- Description:
- Let $G$ be an Archimedean $\ell $-group. We denote by $G^d$ and $R_D(G)$ the divisible hull of $G$ and the distributive radical of $G$, respectively. In the present note we prove the relation $(R_D(G))^d=R_D(G^d)$. As an application, we show that if $G$ is Archimedean, then it is completely distributive if and only if it can be regularly embedded into a completely distributive vector lattice.
- Rights:
- http://creativecommons.org/publicdomain/mark/1.0/ and policy:public