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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  1. Bandelt H.-J., Tolerance relations on lattices, Bull. Austral. Math. Soc. 23 (1981), 367-381. (1981) Zbl0449.06005MR0625179
  2. Burris S., Sankappanavar H.P., A Course in Universal Algebra, Springer, New York, 1981. Zbl0478.08001MR0648287
  3. Chajda I., Algebraic theory of tolerance relations, Univerzita Palackého Olomouc, Olomouc, 1991. Zbl0747.08001
  4. Chajda I., A note on the triangular scheme, East-West J. Math. 3 1 (2001), 79-80. (2001) Zbl1007.08002MR1866645
  5. Chajda I., Horváth E.K., A triangular scheme for congruence distributivity, Acta Math. Sci. Szeged 68 (2002), 29-35. (2002) Zbl0997.08001MR1916565
  6. Chajda I., Czédli G., Horváth E.K., Trapezoid lemma and congruence distributivity, Math. Slovaca 53 (2003), 247-253. (2003) Zbl1058.08007MR2025021
  7. Chajda I., Radeleczki S., 0 -conditions and tolerance schemes, Acta Math. Univ. Comenianae 72 2 (2003), 177-184. (2003) Zbl1087.08002MR2040261
  8. Czédli G., Horváth E.K., Congruence distributivity and modularity permit tolerances, Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41 (2002), 43-53. (2002) Zbl1043.08002MR1967339
  9. Czédli G., Lenkehegyi A., On classes of ordered algebras and quasiorder distributivity, Acta Sci. Math. 46 (1983), 41-54. (1983) MR0739021
  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
  11. Grillet P.A., Varlet J.C., Complementedness conditions in lattices, Bull. Soc. Roy. Sci. Liège 36 (1967), 628-642. (1967) Zbl0157.34202MR0228389
  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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