Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties

Gábor Czédli; Eszter K. Horváth

Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica (2002)

  • Volume: 41, Issue: 1, page 43-53
  • ISSN: 0231-9721

How to cite

top

Czédli, Gábor, and Horváth, Eszter K.. "Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties." Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica 41.1 (2002): 43-53. <http://eudml.org/doc/23733>.

@article{Czédli2002,
author = {Czédli, Gábor, Horváth, Eszter K.},
journal = {Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica},
keywords = {congruence modularity; Mal'tsev condition; lattice identity; tolerance relation; Day terms; Jónsson terms},
language = {eng},
number = {1},
pages = {43-53},
publisher = {Palacký University Olomouc},
title = {Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties},
url = {http://eudml.org/doc/23733},
volume = {41},
year = {2002},
}

TY - JOUR
AU - Czédli, Gábor
AU - Horváth, Eszter K.
TI - Reflexive relations and Mal'tsev conditions for congruence lattice identities in modular varieties
JO - Acta Universitatis Palackianae Olomucensis. Facultas Rerum Naturalium. Mathematica
PY - 2002
PB - Palacký University Olomouc
VL - 41
IS - 1
SP - 43
EP - 53
LA - eng
KW - congruence modularity; Mal'tsev condition; lattice identity; tolerance relation; Day terms; Jónsson terms
UR - http://eudml.org/doc/23733
ER -

References

top
  1. Czédli G., Freese R., On congruence distributivity and modularity, Algebra Universalis 17 (1983), 216-219. (1983) Zbl0548.08003MR0726275
  2. Czédli G., Horváth E. K., Congruence distributivity and modularity permit tolerances, Acta Univ. Palacki. Olomuc., Fac. rer. nat., Math., to appear. Zbl1043.08002MR1967338
  3. Czédli G., Horváth E. K., All congruence lattice identities implying modularity have Mal’tsev conditions, Algebra Universalis, to appear. Zbl1091.08007
  4. Day A., A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull. 12 (1969), 167-173. (1969) MR0248063
  5. Day A., p-modularity implies modularity in equational classes, Algebra Universalis 3 (1973), 398-399. (1973) Zbl0288.06012MR0354497
  6. Day A., Freese R., A characterization of identities implying congruence modularity, I. Canad. J. Math. 32 (1980), 1140-1167. (1980) Zbl0414.08003MR0596102
  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. (1987) Zbl0636.08001MR0909290
  8. Freese R., Nation J. B., 3,3 Lattice inclusions imply congruence modularity, Algebra Universalis 7 (1977), 191-194. (1977) Zbl0384.08006MR0434906
  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. (1972) Zbl0264.06008MR0313169
  10. Grätzer G., Two Mal’cev-type theorems in universal algebra, J. Combinatorial Theory 8 (1970), 334-342. (1970) 
  11. Gumm H. P., Geometrical methods in congruence modular algebras, Mem. Amer. Math. Soc. 45, 286 (1983), viii+79. (1983) Zbl0547.08006MR0714648
  12. Herrmann C., Huhn A. P., Zum Begriff der Charakteristik modularer Verbände, Math. Z. 144 (1975), 185-194. (1975) Zbl0316.06006MR0384630
  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. (1974) MR0447064
  14. Huhn A. P., Schwach distributive Verbände, I. Acta Sci. Math. (Szeged) 33 (1.972), 297-305 (in German). Zbl0536.08002MR0337710
  15. Huhn A. P., On Gratzer's problem concerning automorphisms of a finitely presented lattice, Algebra Universalis 5 (1975), 65-71. (1975) MR0392713
  16. Hutchinson G., Czédli G., A test for identities satisfied in lattices of submodules, Algebra Universalis 8 (1978), 269-309. (1978) MR0469840
  17. Jónsson B., Algebras whose congruence lattices are distributive, Math. Scandinavica 21 (1967), 110-121. (1967) MR0237402
  18. Jónsson B., Congruence varieties, Algebra Universalis 10 (1980), 355-394. (1980) MR0564122
  19. McKenzie R., Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc. 174 (1972), 1-43. (1972) MR0313141
  20. Mederly P., Three Mal’cev type theorems and their application, Mat. časopis SAV 25 (1975), 83-95. (1975) Zbl0302.08003MR0384650
  21. Nation J. B., Varieties whose congruences satisfy certain lattice identities, Algebra Universalis 4 (1974), 78-88. (1974) Zbl0299.08002MR0354501
  22. Neumann W. D., On Malcev conditions, J. Austral. Math. Soc. 17 (1974), 376-384. (1974) Zbl0294.08004MR0371781
  23. Pálfy P. P., Szabó, Cs., An identity for subgroup lattices of abelian groups, Algebra Universalis 33 (1995), 191-195. (1995) Zbl0820.06003MR1318983
  24. Pixley A. F., Local Malcev conditions, Canad. Math. Bull. 15 (1972), 559-568. (1972) Zbl0254.08009MR0309837
  25. Snow J. W., Mal’tsev conditions and relations on algebras, Algebra Universalis 42 (1999), 299-309. (1999) Zbl0979.08004MR1759488
  26. Taylor W., Characterizing Mal’cev conditions, Algebra Universalis 3 (1973), 351-397. (1973) Zbl0304.08003MR0349537
  27. Wille R., Kongruenzklassengeometrien, Lecture Notes in Mathematics 113, Springer-Verlag, Berlin-New York, 1970, iii+99 (in German). (1970) Zbl0191.51403MR0262149

NotesEmbed ?

top

You must be logged in to post comments.

To embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.

Only the controls for the widget will be shown in your chosen language. Notes will be shown in their authored language.

Tells the widget how many notes to show per page. You can cycle through additional notes using the next and previous controls.

    
                

                
Note: Best practice suggests putting the JavaScript code just before the closing </body> tag.