| Title:
|
Sequential convergences on free lattice ordered groups (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
117 |
| Issue:
|
1 |
| Year:
|
1992 |
| Pages:
|
48-54 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In this paper the partially ordered set Conv $G$ of all sequential convergences on $G$ is investigated, where $G$ is either a free lattice ordered group or a free abelian lattice ordered group. (English) |
| Keyword:
|
free lattice-ordered group |
| Keyword:
|
compatible sequential convergences |
| Keyword:
|
atom |
| Keyword:
|
free abelian lattice ordered group |
| Keyword:
|
sequential convergence |
| MSC:
|
06F15 |
| MSC:
|
06F20 |
| MSC:
|
54H11 |
| idZBL:
|
Zbl 0770.06007 |
| idMR:
|
MR1154054 |
| DOI:
|
10.21136/MB.1992.126229 |
| . |
| Date available:
|
2009-09-24T20:49:48Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/126229 |
| . |
| Reference:
|
[1] M. Anderson T. Feil: Lattice-Ordered Groups, An Introduction.Reidel Publ., Dordrecht, 1988. MR 0937703 |
| Reference:
|
[2] S. Bernau: Free abelian lattice groups.Math. Ann. 150(1969), 48-59. Zbl 0157.36801, MR 0241340 |
| Reference:
|
[3] G. Birkhoff: Lattice Theory.Third Edition, Providence, 1967. Zbl 0153.02501, MR 0227053 |
| Reference:
|
[4] P. Conrad: Free abelian l-groups and vector lattices.Math. Ann. 190 (1971), 306-312. MR 0281667, 10.1007/BF01431159 |
| Reference:
|
[5] P. Conrad: Free lattice-ordered groups.J. Algebra 16 (1970), 191-203. Zbl 0213.31502, MR 0270992, 10.1016/0021-8693(70)90024-4 |
| Reference:
|
[6] P. Conrad: Lattice-Ordered Groups.Tulane Lecture Notes; New Orleans, 1970. Zbl 0258.06011 |
| Reference:
|
[7] R. Frič F. Zanolin: Sequential convergence in free groups.Rend. Ist. Matem. Univ. Trieste 18 (1986), 200-218. MR 0928331 |
| Reference:
|
[8] M. Harminc: Sequential convergences on abelian lattice-ordered groups.Convergence Structures 1984. Mathematical Research, Band 24, Akademie-Verlag, Berlin, 1985, pp. 153-158. MR 0835480 |
| Reference:
|
[9] M. Harminc: The cardinality of the system of all sequential convergences on an abelian lattice ordered group.Czechoslovak Math. J. 31 (1987), 533-546. MR 0913986 |
| Reference:
|
[10] M. Harminc: Sequential convergences on lattice ordered groups.Czechoslov. Math. J 39 (1989), 232-238. MR 0992130 |
| Reference:
|
[11] M. Harminc: Convergences on lattice ordered groups.Dissertation, Math. Inst. Slovak Acad. Sci, 1986. (In Slovak.) |
| Reference:
|
[12] M. Harminc J. Jakubík: Maximal convergences and minimal proper convergences in l-groups.Czechoslov. Math. J. 39 (1989), 631-640. MR 1017998 |
| Reference:
|
[13] J. Jakubík: Convergences and complete distributivity of lattice ordered groups.Math. Slovaca 38 (1988), 269-272. MR 0977905 |
| Reference:
|
[14] J. Jakubík: Lattice ordered groups having a largest convergence.Czechoslov. Math. J. 39 (1989), 717-729. MR 1018008 |
| Reference:
|
[15] B. M. Koпытов: Рещеточно упорядоченные группы.Mocквa, 1984. Zbl 1063.82528 |
| Reference:
|
[16] J. Novák: On a free convergence group..Proc. Conf. on Convergence Structures, Lawton, Oklahoma, 1980, pp. 97-102. MR 0605123 |
| Reference:
|
[17] E. C. Weinberg: Free lattice-ordered abelian groups.Math. Ann. 151 (1963), 187-199. Zbl 0114.25801, MR 0153759, 10.1007/BF01398232 |
| Reference:
|
[18] E. C. Weinberg: Free lattice-ordered abelian groups. II.Math. Ann. 159 (1965), 217-222. Zbl 0138.26201, MR 0181668, 10.1007/BF01362439 |
| . |
