On the distributive radical of an Archimedean lattice-ordered group
Czechoslovak Mathematical Journal (2009)
- Volume: 59, Issue: 3, page 687-693
- ISSN: 0011-4642
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topJakubík, Ján. "On the distributive radical of an Archimedean lattice-ordered group." Czechoslovak Mathematical Journal 59.3 (2009): 687-693. <http://eudml.org/doc/37951>.
@article{Jakubík2009,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Czechoslovak Mathematical Journal},
keywords = {Archimedean $\ell $-group; divisible hull; distributive radical; complete distributivity; Archimedean -group; divisible hull; distributive radical; complete distributivity},
language = {eng},
number = {3},
pages = {687-693},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the distributive radical of an Archimedean lattice-ordered group},
url = {http://eudml.org/doc/37951},
volume = {59},
year = {2009},
}
TY - JOUR
AU - Jakubík, Ján
TI - On the distributive radical of an Archimedean lattice-ordered group
JO - Czechoslovak Mathematical Journal
PY - 2009
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 59
IS - 3
SP - 687
EP - 693
AB - 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.
LA - eng
KW - Archimedean $\ell $-group; divisible hull; distributive radical; complete distributivity; Archimedean -group; divisible hull; distributive radical; complete distributivity
UR - http://eudml.org/doc/37951
ER -
References
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