# Article

 Title: Closed convex $l$-subgroups and radical classes of convergence $l$-groups (English) Author: Jakubík, Ján Language: English Journal: Mathematica Bohemica ISSN: 0862-7959 (print) ISSN: 2464-7136 (online) Volume: 122 Issue: 3 Year: 1997 Pages: 301-315 Summary lang: English . Category: math . Summary: In this paper we prove that the system of all closed convex $\ell$-subgroups of a convergence $\ell$-group is a Brouwer lattice and that a similar result is valid for radical classes of convergence $\ell$-groups. (English) Keyword: radical class of cl-groups Keyword: Brouwer lattice Keyword: convergence $\ell$-group Keyword: closed convex $\ell$-subgroup Keyword: radical class of convergence $\ell$-groups MSC: 06F20 MSC: 22C05 idZBL: Zbl 0897.06022 idMR: MR1600660 DOI: 10.21136/MB.1997.126146 . Date available: 2009-09-24T21:26:46Z Last updated: 2020-07-29 Stable URL: http://hdl.handle.net/10338.dmlcz/126146 . Reference: [1] P. Conrad: K-radical classes of lattice ordered groups.Algebra, Proc. Conf. Carbondale (1980), Lecture Notes Math. 81,8 (1981), 186-207. MR 0613186 Reference: [2] M. Darnel: Closure operations on radicals of lattice ordered groups.Czechoslovak Math. J. 37 (1987), 51-64. MR 0875127 Reference: [3] R. Frič V. Koutník: Sequential convergence spaces: Iteration, extension, completion, enlargement.Recent Progress in General Topology. Elsevier Sci. Publ., Amsterdam, 1992, pp. 201-213. MR 1229126 Reference: [4] J. Jakubík: Direct decompositions of partially ordered groups, II.Czechoslovak Math. J. 11 (1961), 490-515. (In Russian.) MR 0137776 Reference: [5] J. Jakubík: Radical mappings and radical classes of lattice ordered groups.Symposia Math. 21. Academic Press, New York, 1977, pp. 451-477. MR 0491397 Reference: [6] J. Jakubík: Sequential convergences in l-groups without Urysohn's axiom.Czechoslovak Math. J. 42 (1992), 101-116. Zbl 0770.06008, MR 1152174 Reference: [7] N. Ya. Medvedev: On the lattice of radicals of a finitely generated l-group.Math. Slovaca 33 (1983), 185-188. (In Russian.) MR 0699088 Reference: [8] Dao-Rong Ton: Product radical classes of l-groups.Czechoslovak Math. J. 42 (1992), 129-142. MR 1152176 .

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