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Special-valued l-groups and Abelian covers. (English) Zbl 0627.06014
Author’s abstract: “This paper represents a new and independent proof of the theorem [proven first by V. M. Kopytov and S. A. Gurchenkov, Sib. Mat. Zh. 28, No.3(163), 66-69 (1987; Zbl 0622.06014)] and again by N. R. Reilly [Order 3, 287-297 (1986; Zbl 0616.06016)] that covers of the Abelian l-variety are either representable or are Scrimger covers. The proof in this paper is based upon the l-Cauchy constructions of R. N. Ball [Trans. Am. Math. Soc. 259, 357-392 (1980; Zbl 0441.06015)]; once these are applied to the problem, the proof becomes elementary.”
Reviewer: F.Šik

06F15 Ordered groups
06B20 Varieties of lattices
08B15 Lattices of varieties
20E10 Quasivarieties and varieties of groups
20F60 Ordered groups (group-theoretic aspects)
Full Text: DOI
[1] R. N. Ball (1980) Convergence and Cauchy structures on lattice-ordered groups, Trans. Amer. Math. Soc. 259, 357-391. · Zbl 0441.06015
[2] R. N. Ball, P. Conrad, and M. Darnel (1986) Above and below subgroups of a lattice-ordered group, Trans. Amer. Math. Soc. 297, 1-40. · Zbl 0628.06013
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[10] N. Reilly (1986) Varieties of lattice-ordered groups that contain no Abelian o-groups are solvable, Order, 3, 287-297. · Zbl 0616.06016
[11] E. B. Scrimger (1975) A large class of small varieties of lattice-ordered groups, Proc. Amer. Math. Soc. 51, 301-306. · Zbl 0312.06010
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