Closed convex l -subgroups and radical classes of convergence l -groups

Ján Jakubík

Mathematica Bohemica (1997)

  • Volume: 122, Issue: 3, page 301-315
  • ISSN: 0862-7959

Abstract

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In this paper we prove that the system of all closed convex ℓ -subgroups of a convergence ℓ -group is a Brouwer lattice and that a similar result is valid for radical classes of convergence ℓ -groups.

How to cite

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Jakubík, Ján. "Closed convex $l$-subgroups and radical classes of convergence $l$-groups." Mathematica Bohemica 122.3 (1997): 301-315. <http://eudml.org/doc/248153>.

@article{Jakubík1997,
abstract = {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.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {radical class of cl-groups; Brouwer lattice; convergence $\ell $-group; closed convex $\ell $-subgroup; radical class of convergence $\ell $-groups; convergence -group; closed convex -subgroup; radical class of cl-groups; Brouwer lattice},
language = {eng},
number = {3},
pages = {301-315},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Closed convex $l$-subgroups and radical classes of convergence $l$-groups},
url = {http://eudml.org/doc/248153},
volume = {122},
year = {1997},
}

TY - JOUR
AU - Jakubík, Ján
TI - Closed convex $l$-subgroups and radical classes of convergence $l$-groups
JO - Mathematica Bohemica
PY - 1997
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 122
IS - 3
SP - 301
EP - 315
AB - 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.
LA - eng
KW - radical class of cl-groups; Brouwer lattice; convergence $\ell $-group; closed convex $\ell $-subgroup; radical class of convergence $\ell $-groups; convergence -group; closed convex -subgroup; radical class of cl-groups; Brouwer lattice
UR - http://eudml.org/doc/248153
ER -

References

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  1. P. Conrad, K-radical classes of lattice ordered groups, Algebra, Proc. Conf. Carbondale (1980), Lecture Notes Math. 81,8 (1981), 186-207. (1980) MR0613186
  2. M. Darnel, Closure operations on radicals of lattice ordered groups, Czechoslovak Math. J. 37 (1987), 51-64. (1987) MR0875127
  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. (1992) MR1229126
  4. J. Jakubík, Direct decompositions of partially ordered groups, II, Czechoslovak Math. J. 11 (1961), 490-515. (In Russian.) (1961) MR0137776
  5. J. Jakubík, Radical mappings and radical classes of lattice ordered groups, Symposia Math. 21. Academic Press, New York, 1977, pp. 451-477. (1977) MR0491397
  6. J. Jakubík, Sequential convergences in l-groups without Urysohn's axiom, Czechoslovak Math. J. 42 (1992), 101-116. (1992) Zbl0770.06008MR1152174
  7. N. Ya. Medvedev, On the lattice of radicals of a finitely generated l-group, Math. Slovaca 33 (1983), 185-188. (In Russian.) (1983) MR0699088
  8. Dao-Rong Ton, Product radical classes of l-groups, Czechoslovak Math. J. 42 (1992), 129-142. (1992) MR1152176

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