Congruence schemes and their applications

Ivan Chajda; Sándor Radelecki

Commentationes Mathematicae Universitatis Carolinae (2005)

  • Volume: 46, Issue: 1, page 1-14
  • ISSN: 0010-2628

Abstract

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Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.

How to cite

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Chajda, Ivan, and Radelecki, Sándor. "Congruence schemes and their applications." Commentationes Mathematicae Universitatis Carolinae 46.1 (2005): 1-14. <http://eudml.org/doc/249539>.

@article{Chajda2005,
abstract = {Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'\{e\}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.},
author = {Chajda, Ivan, Radelecki, Sándor},
journal = {Commentationes Mathematicae Universitatis Carolinae},
keywords = {congruence schemes; majority algebra; tolerance lattice; 0-conditions; majority algebra; tolerance lattice},
language = {eng},
number = {1},
pages = {1-14},
publisher = {Charles University in Prague, Faculty of Mathematics and Physics},
title = {Congruence schemes and their applications},
url = {http://eudml.org/doc/249539},
volume = {46},
year = {2005},
}

TY - JOUR
AU - Chajda, Ivan
AU - Radelecki, Sándor
TI - Congruence schemes and their applications
JO - Commentationes Mathematicae Universitatis Carolinae
PY - 2005
PB - Charles University in Prague, Faculty of Mathematics and Physics
VL - 46
IS - 1
SP - 1
EP - 14
AB - Using congruence schemes we formulate new characterizations of congruence distributive, arithmetical and majority algebras. We prove new properties of the tolerance lattice and of the lattice of compatible reflexive relations of a majority algebra and generalize earlier results of H.-J. Bandelt, G. Cz'{e}dli and the present authors. Algebras whose congruence lattices satisfy certain 0-conditions are also studied.
LA - eng
KW - congruence schemes; majority algebra; tolerance lattice; 0-conditions; majority algebra; tolerance lattice
UR - http://eudml.org/doc/249539
ER -

References

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  10. Czédli G., Horváth E.K., Radeleczki S., On tolerance lattices of algebras in congruence modular varieties, Acta Math. Hungar. 100 (1-2) (2003), 9-17. (2003) Zbl1049.08007MR1984855
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  12. Gumm H.-P., Geometrical methods in congruence modular algebras, Mem. Amer. Math. Soc. 45 286 (1983). (1983) Zbl0547.08006MR0714648
  13. Pinus A.G., Chajda I., Quasiorders on universal algebras, Algebra i Logika 32 3 (1993), 308-325 (in Russian). (1993) Zbl0824.08002MR1286557
  14. Radeleczki S., Schweigert D., Lattices with complemented tolerance lattice, Czechoslovak Math. J. 54 (129) (2004), 2 407-412. (2004) Zbl1080.06006MR2059261
  15. Stern M., Semimodular Lattices, Theory and Applications, Cambridge University Press, Cambridge, New York, Melbourne, 1999. MR1695504
  16. Varlet J.C., A generalization of the notion of pseudo-complementedness, Bull. Soc. Roy. Sci. Liège 37 (1968), 149-158. (1968) Zbl0162.03501MR0228390

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