| Title:
|
On the congruence lattice of an abelian lattice ordered group (English) |
| Author:
|
Jakubík, Ján |
| Language:
|
English |
| Journal:
|
Mathematica Bohemica |
| ISSN:
|
0862-7959 (print) |
| ISSN:
|
2464-7136 (online) |
| Volume:
|
126 |
| Issue:
|
3 |
| Year:
|
2001 |
| Pages:
|
653-660 |
| Summary lang:
|
English |
| . |
| Category:
|
math |
| . |
| Summary:
|
In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group. (English) |
| Keyword:
|
lattice ordered group |
| Keyword:
|
$\ell $-ideal |
| Keyword:
|
congruence lattice |
| Keyword:
|
disjoint subset |
| MSC:
|
06B10 |
| MSC:
|
06B15 |
| MSC:
|
06F20 |
| idZBL:
|
Zbl 0978.06010 |
| idMR:
|
MR1970268 |
| DOI:
|
10.21136/MB.2001.134195 |
| . |
| Date available:
|
2009-09-24T21:55:38Z |
| Last updated:
|
2020-07-29 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/134195 |
| . |
| Reference:
|
[1] G. Birkhoff: Lattice Theory.Revised Edition, Providence, 1948. Zbl 0033.10103, MR 0029876 |
| Reference:
|
[2] P. Conrad: The structure of a lattice ordered group with a finite number of disjoint elements.Michigan Math. J. 7 (1960), 171–182. Zbl 0103.01501, MR 0116059, 10.1307/mmj/1028998387 |
| Reference:
|
[3] P. Conrad: Lattice Ordered Groups.Tulane University, 1970. Zbl 0258.06011 |
| Reference:
|
[4] G. Grätzer: On the congruence lattice of a lattice.In: The Dilworth Theorems. Selected Papers of Robert P. Dilworth, K. Bogart, R. Freese, J. Kung (eds.), Birkhäuser Verlag, Basel, 1990, pp. 460–464. MR 1111511 |
| Reference:
|
[5] G. Grätzer, E. T. Schmidt: On congruence lattices of lattices.Acta Math. Acad. Sci. Hungar. 13 (1962), 179–185. MR 0139551, 10.1007/BF02033636 |
| Reference:
|
[6] K. Iwasawa: On linearly ordered groups.J. Math. Soc. Japan 1 (1948), 1–9. Zbl 0038.01301, MR 0028313, 10.2969/jmsj/00110001 |
| Reference:
|
[7] J. Jakubík: On lexico extensions of lattice ordered groups.Math. Slovaca 33 (1983), 81–84. MR 0689282 |
| Reference:
|
[8] M. Ploščica, J. Tůma, F. Wehrung: Congruence lattices of free lattices in non-distributive varieties.Colloq. Math. 76 (1998), 269–278. MR 1618712, 10.4064/cm-76-2-269-278 |
| . |
