×

zbMATH — the first resource for mathematics

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

MSC:
06F15 Ordered groups
06B20 Varieties of lattices
08B15 Lattices of varieties
20E10 Quasivarieties and varieties of groups
20F60 Ordered groups (group-theoretic aspects)
PDF BibTeX XML Cite
Full Text: DOI
References:
[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
[3] A. Bigard, K. Keimel, and S. Wolfenstein (1977) Groupes et Anneaux Reticulés, Lecture Notes in Mathematics, No. 608, Springer-Verlag, New York. · Zbl 0384.06022
[4] J. P. Bixler and M. Darnel (1986) Special-valued l-groups, Algebra Universalis 22, 172-191. · Zbl 0597.06014
[5] A. Glass, W. C. Holland, and S. McCleary (1980) The structure of l-group varieties, Algebra Universalis 10, 1-20. · Zbl 0439.06013
[6] S. A. Gurchenkov (1982) Minimal varieties of l-groups, Algebra i Logika, 21 (2), 131-137.
[7] S. A. Gurchenkov and V. Kopytov (1987) On covers of the variety of Abelian lattice-ordered groups, Siberian Math. J. 28 (3), · Zbl 0632.06023
[8] W. C. Holland (1976) The largest proper variety of lattice-ordered groups, Proc. Amer. Math. Soc. 57, 25-28. · Zbl 0339.06011
[9] N. Ya. Medvedev (1977) The lattices of varieties of lattice-ordered groups and Lie algebras, Algebra i Logika 16 (1), 40-45.
[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
[12] J. E. Smith (1980) The lattice of l-group varieties, Trans. Amer. Math. Soc. 257, 347-357. · Zbl 0459.06007
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.