zbMATH — the first resource for mathematics

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

MSC:
 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces 08B15 Lattices of varieties
Full Text:
References:
 [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
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.