| Title:
|
Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties (English) |
| Author:
|
Czédli, Gábor |
| Author:
|
Horváth, Eszter K. |
| Language:
|
English |
| Journal:
|
Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica |
| ISSN:
|
0231-9721 |
| Volume:
|
41 |
| Issue:
|
1 |
| Year:
|
2002 |
| Pages:
|
43-53 |
| . |
| Category:
|
math |
| . |
| MSC:
|
08B05 |
| MSC:
|
08B10 |
| idZBL:
|
Zbl 1038.18001 |
| idMR:
|
MR1967339 |
| . |
| Date available:
|
2009-01-29T16:02:16Z |
| Last updated:
|
2012-05-04 |
| Stable URL:
|
http://hdl.handle.net/10338.dmlcz/120454 |
| . |
| Reference:
|
[1] Czédli G., Freese R.: On congruence distributivity and modularity.Algebra Universalis 17 (1983), 216-219. Zbl 0548.08003, MR 0726275 |
| Reference:
|
[2] Czédli G., Horváth E. K.: Congruence distributivity and modularity permit tolerances.Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math., to appear. Zbl 1043.08002, MR 1967338 |
| Reference:
|
[3] Czédli G., Horváth E. K.: All congruence lattice identities implying modularity have Mal’tsev conditions.Algebra Universalis, to appear. Zbl 1091.08007 |
| Reference:
|
[4] Day A.: A characterization of modularity for congruence lattices of algebras.Canad. Math. Bull. 12 (1969), 167-173. MR 0248063 |
| Reference:
|
[5] Day A.: p-modularity implies modularity in equational classes.Algebra Universalis 3 (1973), 398-399. Zbl 0288.06012, MR 0354497 |
| Reference:
|
[6] Day A., Freese R.: A characterization of identities implying congruence modularity.I. Canad. J. Math. 32 (1980), 1140-1167. Zbl 0414.08003, MR 0596102 |
| Reference:
|
[7] Freese R., McKenzie R.: Commutator theory for congruence modular varieties.London Mathematical Society Lecture Note Series, 125, Cambridge University Press, Cambridge, 1987. iv+227. Zbl 0636.08001, MR 0909290 |
| Reference:
|
[8] Freese R., Nation J. B.: 3,3 Lattice inclusions imply congruence modularity.Algebra Universalis 7 (1977), 191-194. Zbl 0384.08006, MR 0434906 |
| Reference:
|
[9] Gedeonová E.: A characterization of p-modularity for congruence lattices of algebras.Acta Fac. Rerum Natur. Univ. Comenian. Math. Publ. 28 (1972), 99-106. Zbl 0264.06008, MR 0313169 |
| Reference:
|
[10] Grätzer G.: Two Mal’cev-type theorems in universal algebra.J. Combinatorial Theory 8 (1970), 334-342. |
| Reference:
|
[11] Gumm H. P.: Geometrical methods in congruence modular algebras.Mem. Amer. Math. Soc. 45, 286 (1983), viii+79. Zbl 0547.08006, MR 0714648 |
| Reference:
|
[12] Herrmann C., Huhn A. P.: Zum Begriff der Charakteristik modularer Verbände.Math. Z. 144 (1975), 185-194. Zbl 0316.06006, MR 0384630 |
| Reference:
|
[13] Herrmann C., Huhn A. P.: Lattices of normal subgroups which are generated by frames.In: Lattice Theory, Proc. Conf. Szeged 1974, Coll. Math. Soc. J. Bolyai 12, North-Holland, Amsterdam 1976, 97-136. MR 0447064 |
| Reference:
|
[14] Huhn A. P.: Schwach distributive Verbände.I. Acta Sci. Math. (Szeged) 33 (1.972), 297-305 (in German). Zbl 0536.08002, MR 0337710 |
| Reference:
|
[15] Huhn A. P.: On Gratzer's problem concerning automorphisms of a finitely presented lattice.Algebra Universalis 5 (1975), 65-71. MR 0392713 |
| Reference:
|
[16] Hutchinson G., Czédli G.: A test for identities satisfied in lattices of submodules.Algebra Universalis 8 (1978), 269-309. MR 0469840 |
| Reference:
|
[17] Jónsson B.: Algebras whose congruence lattices are distributive.Math. Scandinavica 21 (1967), 110-121. MR 0237402 |
| Reference:
|
[18] Jónsson B.: Congruence varieties.Algebra Universalis 10 (1980), 355-394. MR 0564122 |
| Reference:
|
[19] McKenzie R.: Equational bases and nonmodular lattice varieties.Trans. Amer. Math. Soc. 174 (1972), 1-43. MR 0313141 |
| Reference:
|
[20] Mederly P.: Three Mal’cev type theorems and their application.Mat. časopis SAV 25 (1975), 83-95. Zbl 0302.08003, MR 0384650 |
| Reference:
|
[21] Nation J. B.: Varieties whose congruences satisfy certain lattice identities.Algebra Universalis 4 (1974), 78-88. Zbl 0299.08002, MR 0354501 |
| Reference:
|
[22] Neumann W. D.: On Malcev conditions.J. Austral. Math. Soc. 17 (1974), 376-384. Zbl 0294.08004, MR 0371781 |
| Reference:
|
[23] Pálfy P. P., Szabó, Cs.: An identity for subgroup lattices of abelian groups.Algebra Universalis 33 (1995), 191-195. Zbl 0820.06003, MR 1318983 |
| Reference:
|
[24] Pixley A. F.: Local Malcev conditions.Canad. Math. Bull. 15 (1972), 559-568. Zbl 0254.08009, MR 0309837 |
| Reference:
|
[25] Snow J. W.: Mal’tsev conditions and relations on algebras.Algebra Universalis 42 (1999), 299-309. Zbl 0979.08004, MR 1759488 |
| Reference:
|
[26] Taylor W.: Characterizing Mal’cev conditions.Algebra Universalis 3 (1973), 351-397. Zbl 0304.08003, MR 0349537 |
| Reference:
|
[27] Wille R.: Kongruenzklassengeometrien.Lecture Notes in Mathematics 113, Springer-Verlag, Berlin-New York, 1970, iii+99 (in German). Zbl 0191.51403, MR 0262149 |
| . |
