Anderson, M.; Darnel, M.; Feil, T. A variety of lattice-ordered groups containing all representable covers of the abelian variety. (English) Zbl 0738.06015 Order 7, No. 4, 401-405 (1991). A variety of lattice-ordered groups having the property described in the title has been described by N. Ya. Medvedev [Czech. Math. J. 34(109), 6-17 (1984; Zbl 0551.06017)]. The present authors have found another variety having the mentioned property; the description of this variety is simpler than in the case of the variety considered by Medvedev. Reviewer: J.Jakubík (Košice) Cited in 5 Documents MSC: 06F15 Ordered groups 06B20 Varieties of lattices 06F20 Ordered abelian groups, Riesz groups, ordered linear spaces Keywords:representable cover; abelian variety; variety of lattice-ordered groups Citations:Zbl 0551.06017 PDFBibTeX XMLCite \textit{M. Anderson} et al., Order 7, No. 4, 401--405 (1991; Zbl 0738.06015) Full Text: DOI References: [1] M.Anderson and T.Feil (1988) Lattice-Ordered Groups: An Introduction, D. Reidel, Dordecht, Holland. · Zbl 0636.06008 [2] G.Bergman (1984) Specially ordered groups, Comm. Algebra 12, 2315-1333. · Zbl 0537.06014 [3] C. G.Chehata (1952) An algebraically simple ordered group, Proc. London Math. Soc. 2, 183-197. · Zbl 0046.02501 [4] C. G.Chehata (1958) On a theorem on ordered groups, Proc. Glasgow Math. Assoc. 4, 16-21. · Zbl 0198.05102 [5] A. H.Clifford (1952) A noncommutative ordinally simple linearly ordered group, Proc. Amer. Math. Soc. 2, 902-903. · Zbl 0044.01301 [6] M.Darnel (1987) Special-valued l-groups and abelian covers, Order 4, 191-194. · Zbl 0627.06014 [7] T.Feil (1980) A comparison of Chehata’s and Clifford’s ordinally simple ordered groups, Proc. Amer. Math. Soc. 79, 512-514. · Zbl 0457.20042 [8] T.Feil (1982) An uncountable tower of l-group varieties, Algebra Universalis 14, 129-131. · Zbl 0438.06003 [9] S. A. Gurchenkov and V. M. Kopytov (1987) On covers of the variety of abelian lattice-ordered groups (in Russian), Siberian Math. J. 28. · Zbl 0632.06023 [10] H.Hollister (1972) Nilpotent l-groups are representable, Algebra Universalis 8, 65-71. · Zbl 0385.06024 [11] V. M. Kopytov, Nilpotent lattice-ordered groups, Sibirsk. Mat. Zh. 23, 127-131, 224. · Zbl 0511.06011 [12] N. Ya.Medvedev (1977) Varieties of lattice-ordered groups (Russian), Algebra i Logika 16, 40-45. [13] N. YaMedvedev (1984) Lattice of o-approximable l-varieties (Russian), Czech. Math. J. 34(109), 6-17. [14] N.Reilly (1983) Nilpotent, weakly abelian and Hamiltonian lattice-ordered groups, Czech. Math. J. 33(108), 348-353. · Zbl 0553.06020 [15] N.Reilly (1986) Varieties of lattice-ordered groups that contain no non-abelian o-groups are solvable, Order 3, 287-297. · Zbl 0616.06016 [16] E. B.Scrimger (1975) A large class of small varieties of lattice-ordered groups. Proc. Amer. Math. Soc. 51, 301-306. · Zbl 0312.06010 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. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.