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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:
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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


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