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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  1. Lattice Theory, Revised Edition, Providence, 1948. (1948) Zbl0033.10103MR0029876
  2. The structure of a lattice ordered group with a finite number of disjoint elements, Michigan Math. J. 7 (1960), 171–182. (1960) Zbl0103.01501MR0116059
  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. On congruence lattices of lattices, Acta Math. Acad. Sci. Hungar. 13 (1962), 179–185. (1962) MR0139551
  6. On linearly ordered groups, J. Math. Soc. Japan 1 (1948), 1–9. (1948) Zbl0038.01301MR0028313
  7. On lexico extensions of lattice ordered groups, Math. Slovaca 33 (1983), 81–84. (1983) MR0689282
  8. Congruence lattices of free lattices in non-distributive varieties, Colloq. Math. 76 (1998), 269–278. (1998) MR1618712

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