Article
Keywords:
radical class of cl-groups; Brouwer lattice; convergence $\ell$-group; closed convex $\ell$-subgroup; radical class of convergence $\ell$-groups
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.
References:
[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
[2] M. Darnel:
Closure operations on radicals of lattice ordered groups. Czechoslovak Math. J. 37 (1987), 51-64.
MR 0875127
[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
[4] J. Jakubík:
Direct decompositions of partially ordered groups, II. Czechoslovak Math. J. 11 (1961), 490-515. (In Russian.)
MR 0137776
[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
[6] J. Jakubík:
Sequential convergences in l-groups without Urysohn's axiom. Czechoslovak Math. J. 42 (1992), 101-116.
MR 1152174 |
Zbl 0770.06008
[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
[8] Dao-Rong Ton:
Product radical classes of l-groups. Czechoslovak Math. J. 42 (1992), 129-142.
MR 1152176