On the congruence lattice of an abelian lattice ordered group

Ján Jakubík

Mathematica Bohemica (2001)

  • Volume: 126, Issue: 3, page 653-660
  • ISSN: 0862-7959

Abstract

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In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.

How to cite

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Jakubík, Ján. "On the congruence lattice of an abelian lattice ordered group." Mathematica Bohemica 126.3 (2001): 653-660. <http://eudml.org/doc/248880>.

@article{Jakubík2001,
abstract = {In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.},
author = {Jakubík, Ján},
journal = {Mathematica Bohemica},
keywords = {lattice ordered group; $\ell $-ideal; congruence lattice; disjoint subset; abelian lattice ordered group; -ideal; congruence lattice; disjoint subset},
language = {eng},
number = {3},
pages = {653-660},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {On the congruence lattice of an abelian lattice ordered group},
url = {http://eudml.org/doc/248880},
volume = {126},
year = {2001},
}

TY - JOUR
AU - Jakubík, Ján
TI - On the congruence lattice of an abelian lattice ordered group
JO - Mathematica Bohemica
PY - 2001
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 126
IS - 3
SP - 653
EP - 660
AB - In the present note we characterize finite lattices which are isomorphic to the congruence lattice of an abelian lattice ordered group.
LA - eng
KW - lattice ordered group; $\ell $-ideal; congruence lattice; disjoint subset; abelian lattice ordered group; -ideal; congruence lattice; disjoint subset
UR - http://eudml.org/doc/248880
ER -

References

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  3. Lattice Ordered Groups, Tulane University, 1970. (1970) Zbl0258.06011
  4. 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. (1990) MR1111511
  5. 10.1007/BF02033636, Acta Math. Acad. Sci. Hungar. 13 (1962), 179–185. (1962) MR0139551DOI10.1007/BF02033636
  6. 10.2969/jmsj/00110001, J. Math. Soc. Japan 1 (1948), 1–9. (1948) Zbl0038.01301MR0028313DOI10.2969/jmsj/00110001
  7. On lexico extensions of lattice ordered groups, Math. Slovaca 33 (1983), 81–84. (1983) MR0689282
  8. 10.4064/cm-76-2-269-278, Colloq. Math. 76 (1998), 269–278. (1998) MR1618712DOI10.4064/cm-76-2-269-278

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