# 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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