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Zbl 1057.06008
Jakub\'ik, Ján
On absolute retracts and absolute convex retracts in some classes of $\ell$-groups. (English)
[J] Discuss. Math., Gen. Algebra Appl. 23, No. 1, 19-30 (2003). ISSN 1509-9415; ISSN 2084-0373/e

If $\cal{C}$ is a class of algebras and $A\in \cal{C}$, then $A$ is called an absolute retract in $\cal{C}$ if, whenever $B\in \cal{C}$ and $A$ is a subalgebra of $B$, then $A$ is a retract of $B$. If $\cal{C}$ is particularly a class of lattice-ordered groups ($\ell $-groups) and $A\in \cal{C}$, then $A$ is called an absolute convex retract in $\cal{C}$, if, whenever $A$ is a convex $\ell $-subgroup of $B$, then $A$ is a retract of $B$. The author describes absolute retracts and absolute convex retracts in the classes of all archimedean $\ell $-groups and complete $\ell $-groups.
[Jiř{\'\i} Rach\uu nek (Olomouc)]

MSC 2000:: *06F20 Ordered abelian groups, etc.
06F15 Ordered groups

Keywords: absolute retract; absolute convex retract; archimedean $\ell $-group; complete $\ell $-group; orthogonal completeness

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