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Covers of the variety of Abelian l-groups. (English) Zbl 0689.06015
The authors construct two covers of the variety A of abelian lattice ordered groups in the lattice of varieties of \(\ell\)-groups. The construction is as follows: Let X be a two-element chain, [X] and \([X]'\) be the free groups over X, equipped with specially constructed orders \(\prec\) and \(\prec '\), respectively, and B and \(B'\) be the varieties generated by [X] and \([X]'\), respectively. Then B and \(B'\) are covers of A.
Reviewer: V.Novák

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
08B15 Lattices of varieties
Full Text: DOI
[1] Bigard A., Groupes et Anneaux Reticules (1977) · Zbl 0384.06022
[2] DOI: 10.1080/00927878408823111 · Zbl 0506.06006
[3] Grätzer G., Universal Algebra (1979)
[4] Feil T., Doctoral dissertation (1980)
[5] Kokorin A.I., Fully Ordered Groups (1974) · Zbl 0131.26403
[6] DOI: 10.1007/BF01669432 · Zbl 0395.06008
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