| 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 |
| . |
