# Article

 Title: Convexities of lattice ordered groups (English) Author: Jakubík, Ján Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 121 Issue: 1 Year: 1996 Pages: 59-67 Summary lang: English . Category: math . Summary: In this paper an injective mapping of the class of all infinite cardinals into the collection of all convexities of lattice ordered groups is constructed; this generalizes an earlier result on convexities of $d$-groups. (English) Keyword: lattice ordered group Keyword: direct product Keyword: convexity of lattice ordered groups Keyword: convex $\ell$-subgroup MSC: 06F15 idZBL: Zbl 0863.06013 idMR: MR1388175 DOI: 10.21136/MB.1996.125936 . Date available: 2009-09-24T21:15:25Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/125936 . Reference: [1] P. Conrad: Torsion radicals of lattice ordered groups.Symposia Math. 31. Academic Press, New York-London, 1977, pp. 479-513. Zbl 0372.06011, MR 0465969 Reference: [2] Dao-Rong Ton: Product radical classes of l-groups.Czechoslovak Math. J. 42 (1992), 129-142. MR 1152176 Reference: [3] J. Jakubík: Radical classes and radical mappings of lattice ordered groups.Symposia Math. 31. Academic Press, New York-London, 1977, pp. 451-477. MR 0491397 Reference: [4] J. Jakubík: On convexities of lattices.Czechoslovak Math. J. 42 (1992), 325-330. MR 1179503 Reference: [5] J. Jakubík: On directed groups with additional operations.Math. Bohem. 118 (1993), 11-17. MR 1213828 Reference: [6] J. Jakubík: On convexities of d-groups.Czechoslovak Math. J. 44 (1994), 305-314. MR 1281025 Reference: [7] V. M. Kopytov, Z. J. Dimitrov: On directed groups.Sibirsk. Mat. Zh. SO (1989), 78-86. (In Russian.) Zbl 0714.06007, MR 1043436 Reference: [8] J. Martinez: Torsion theory of lattice ordered groups.Czechoslovak Math. J. 25 (1975), 284-299. MR 0389705 Reference: [9] R. Mlitz (ed.): General algebra 1980.Proc. Internat. Conf. Krems 1988. North Holland, Amsterdam-New York-Tokyo-Oxford, 1990. MR 1060341 .

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