| Title:
|
Congruence schemes and their applications (English) |
| Author:
|
Chajda, I. |
| Author:
|
Radelecki, S. |
| Language:
|
English |
| Journal:
|
Commentationes Mathematicae Universitatis Carolinae |
| ISSN:
|
0010-2628 (print) |
| ISSN:
|
1213-7243 (online) |
| Volume:
|
46 |
| Issue:
|
1 |
| Year:
|
2005 |
| Pages:
|
1-14 |
| . |
| Category:
|
math |
| . |
| Summary:
|
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. (English) |
| Keyword:
|
congruence schemes |
| Keyword:
|
majority algebra |
| Keyword:
|
tolerance lattice |
| Keyword:
|
0-conditions |
| MSC:
|
06D15 |
| MSC:
|
08A10 |
| MSC:
|
08A30 |
| idZBL:
|
Zbl 1121.08001 |
| idMR:
|
MR2175854 |
| . |
| Date available:
|
2009-05-05T16:49:06Z |
| Last updated:
|
2012-04-30 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/119503 |
| . |
| Reference:
|
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| Reference:
|
[2] Burris S., Sankappanavar H.P.: A Course in Universal Algebra.Springer, New York, 1981. Zbl 0478.08001, MR 0648287 |
| Reference:
|
[3] Chajda I.: Algebraic theory of tolerance relations.Univerzita Palackého Olomouc, Olomouc, 1991. Zbl 0747.08001 |
| Reference:
|
[4] Chajda I.: A note on the triangular scheme.East-West J. Math. 3 1 (2001), 79-80. Zbl 1007.08002, MR 1866645 |
| Reference:
|
[5] Chajda I., Horváth E.K.: A triangular scheme for congruence distributivity.Acta Math. Sci. Szeged 68 (2002), 29-35. Zbl 0997.08001, MR 1916565 |
| Reference:
|
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| Reference:
|
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| Reference:
|
[8] Czédli G., Horváth E.K.: Congruence distributivity and modularity permit tolerances.Acta Univ. Palack. Olomuc. Fac. Rerum Natur. Math. 41 (2002), 43-53. Zbl 1043.08002, MR 1967339 |
| Reference:
|
[9] Czédli G., Lenkehegyi A.: On classes of ordered algebras and quasiorder distributivity.Acta Sci. Math. 46 (1983), 41-54. MR 0739021 |
| Reference:
|
[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. Zbl 1049.08007, MR 1984855 |
| Reference:
|
[11] Grillet P.A., Varlet J.C.: Complementedness conditions in lattices.Bull. Soc. Roy. Sci. Liège 36 (1967), 628-642. Zbl 0157.34202, MR 0228389 |
| Reference:
|
[12] Gumm H.-P.: Geometrical methods in congruence modular algebras.Mem. Amer. Math. Soc. 45 286 (1983). Zbl 0547.08006, MR 0714648 |
| Reference:
|
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| Reference:
|
[14] Radeleczki S., Schweigert D.: Lattices with complemented tolerance lattice.Czechoslovak Math. J. 54 (129) (2004), 2 407-412. Zbl 1080.06006, MR 2059261 |
| Reference:
|
[15] Stern M.: Semimodular Lattices, Theory and Applications.Cambridge University Press, Cambridge, New York, Melbourne, 1999. MR 1695504 |
| Reference:
|
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| . |
