| Title:
             | 
Characterizing tolerance trivial finite algebras (English) | 
| Author:
             | 
Chajda, Ivan | 
| Language:
             | 
English | 
| Journal:
             | 
Archivum Mathematicum | 
| ISSN:
             | 
0044-8753 (print) | 
| ISSN:
             | 
1212-5059 (online) | 
| Volume:
             | 
30 | 
| Issue:
             | 
3 | 
| Year:
             | 
1994 | 
| Pages:
             | 
165-169 | 
| Summary lang:
             | 
English | 
| . | 
| Category:
             | 
math | 
| . | 
| Summary:
             | 
An algebra $A$ is tolerance trivial if $A̰= A$ where $A̰$ is the lattice of all tolerances on $A$. If $A$ contains a Mal’cev function compatible with each $T$ $A̰$, then $A$ is tolerance trivial. We investigate finite algebras satisfying also the converse statement. (English) | 
| Keyword:
             | 
tolerance relation | 
| Keyword:
             | 
finite algebra | 
| Keyword:
             | 
lattice | 
| Keyword:
             | 
tolerance trivial algebra | 
| Keyword:
             | 
Mal’cev function | 
| Keyword:
             | 
Pixley function | 
| Keyword:
             | 
arithmetical algebra | 
| MSC:
             | 
03E20 | 
| MSC:
             | 
08A30 | 
| MSC:
             | 
08A40 | 
| MSC:
             | 
08B05 | 
| idZBL:
             | 
Zbl 0816.08003 | 
| idMR:
             | 
MR1308352 | 
| . | 
| Date available:
             | 
2008-06-06T21:26:21Z | 
| Last updated:
             | 
2012-05-10 | 
| Stable URL:
             | 
http://hdl.handle.net/10338.dmlcz/107505 | 
| . | 
| Reference:
             | 
[1] Abbot, J. C.: Semi-boolean algebra.Matem. Vestnik 4 (1967), 177–198. MR 0239957 | 
| Reference:
             | 
[2] Chajda, I.: Algebraic Theory of Tolerance Relations.Publ. Palacký University Olomouc 1991 (Czech Republic). Zbl 0747.08001 | 
| Reference:
             | 
[3] Chajda, I.: Tolerances in permutable algebras.Czech. Math. J. 38 (1988), 218–225. MR 0946289 | 
| Reference:
             | 
[4] Chajda, I.: On the existence of non-trivial tolerances in permutable algebras.Czech. Math. J. 40 (1990), 598–600. Zbl 0742.08002, MR 1084895 | 
| Reference:
             | 
[5] Chajda, I.: Every at most four element algebra has a Mal’cev theory for permutability.Math. Slovaca 41 (1991), 35–39. Zbl 0779.08001, MR 1094982 | 
| Reference:
             | 
[6] Chajda, I., Czédli, G.: Maltsev functions on small algebras.Studia Sci. Math. Hungarica (Budapest) 28 (1993), 339–348. MR 1266817 | 
| Reference:
             | 
[7] Chajda, I., Niederle, J., Zelinka, B.: On the existence conditions for compatible tolerances.Czech. Math. J. 26 (1976), 304–311. MR 0401561 | 
| Reference:
             | 
[8] Chajda, I., Zelinka, B.: Tolerances and congruences in implication algebras.Czech. Math. J. 38 (1988), 207–217. MR 0946288 | 
| Reference:
             | 
[9] Cornish, W. H.: On Iséki’s BCK-algebras.Lectures Notes in Pure and Appl. Math. 74 (1982), New York, 101–122. Zbl 0486.03033, MR 0647169 | 
| Reference:
             | 
[10] Gumm, H.-P.: Is there a Mal’cev theory for single algebras?.Algebra Univ. 8 (1978), 320–329. Zbl 0382.08003, MR 0472647 | 
| Reference:
             | 
[11] Mal’cev, A. I: On the general theory of algebraic systems (Russian).Matem. Sbornik 35 (1954), 3–20. | 
| Reference:
             | 
[12] Pixley, A. F.: Completeness in arithmetical algebras.Algebra Univ. 2 (1972), 177–192. Zbl 0254.08010, MR 0321843 | 
| Reference:
             | 
[13] Pixley, A. F.: Distributivity and permutability of congruence relations in equational classes of algebras.Proc. Amer. Math. Soc. 14 (1963). Zbl 0113.24804, MR 0146104 | 
| Reference:
             | 
[14] Raftery, J. G., Rosenberg, I. G., Sturm, T.: Tolerance relations and BCK-algebras.Math. Japon. 36 (1991). MR 1109222 | 
| Reference:
             | 
[15] Sturm, T.: On commutative BCK-algebras.Math. Japon. 27 (1982), 197–212. Zbl 0481.03043, MR 0655224 | 
| Reference:
             | 
[16] Tanaka, S.: On $\wedge $-commutative algebras.Math. Semin. Notes Kobe Univ. 3 (1975), 59–64. MR 0419222 | 
| Reference:
             | 
[17] Werner, H.: A Mal’cev condition for admissible relations.Algebra Univ. 3 (1973), 263. Zbl 0276.08004, MR 0330009 | 
| . |