Skip to main content
Log in

Alan Day's early work: congruence identities

  • Published:
algebra universalis Aims and scope Submit manuscript

This is a preview of subscription content, log in via an institution to check access.

Access this article

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

References

  1. Czédli, G. andFreese, R.,On congruence distributivity and modularity, Algebra Universalis17 (1983), 216–219.

    Google Scholar 

  2. Day, A.,A characterization of modularity for congruence lattices of algebras, Canad. Math. Bull.12 (1969), 167–173.

    Google Scholar 

  3. Day, A.,p-modularity implies modularity in equational classes, Algebra Universalis3 (1973), 398–399.

    Google Scholar 

  4. Day, A.,Lattice, conditions implying congruence modularity, Algebra Universalis6 (1976), 291–301.

    Google Scholar 

  5. Day, A.,Splitting lattices generate all lattices, Algebra Universalis7 (1977), 163–170.

    Google Scholar 

  6. Day, A.,Splitting lattices and congruence-modularity, Contributions to universal algebra, Proceedings of the Colloquium held in Szeged, 1975. Colloq. Math. Soc. János Bolyai, vol. 17, North Holland Publishing Co., Amsterdam, 1977, 57–71.

    Google Scholar 

  7. Day, A.,Doubling constructions in lattice theory, Canad. J. Math.44 (1992), 252–269.

    Google Scholar 

  8. Day, A. andKiss, E.,Frames and rings in congruence modular varieties, J. Algebra109 (1987), 479–507.

    Google Scholar 

  9. Day, A. andFreese, R.,A characterization of identities implying congruence modularity, I, Canad. J. Math.32 (1980), 1140–1167.

    Google Scholar 

  10. Dilworth, R. P.,The structure of relatively complemented lattices, Ann. of Math.51 (1950), 348–359.

    Google Scholar 

  11. Freese, R.,Finitely based modular congruence varities are distributive, Algebra Universalis32 (1994), 104–114.

    Google Scholar 

  12. Freese, R., Herrmann, C. andHuhn, A. P.,On some identities valid in Modular congruence varieties, Algebra Universalis12 (1981), 322–334.

    Google Scholar 

  13. Freese, R. andJónsson, B.,Congruence modularity implies the Arguesian identity, Algebra Universalis6 (1976), 225–228.

    Google Scholar 

  14. Freese, R. andMcKenzie, R.,Commutator Theory for Congruence Modular Varieties, London Math. Soc. Lecture Note Series vol.125, Cambridge University Press, Cambridge, 1987.

    Google Scholar 

  15. Freese, R. andNation, J. B.,Congruence lattices of semilattices, Pacific J. Math.49 (1973), 51–58.

    Google Scholar 

  16. Freese, R. andNation, J. B.,3-3 lattice inclusions imply congruence modularity, Algebra Universalis7 (1977), 191–194.

    Google Scholar 

  17. Gedeonová, E.,A characterization of p-modularity for congruence lattices of algebras, Acta Fac. Rerum Natur. Univ. Comenian. Math. Publ.28 (1972), 99–106.

    Google Scholar 

  18. Hagemann, J. andHerrmann, C.,A concrete ideal multiplication for algebraic systems and its relation to congruence distributivity, Arch. Math. (Basel)32 (1979), 234–245.

    Google Scholar 

  19. Hobby, D. andMcKenzie, R.,The Structure of Finite Algebras (tame congruence theory), Contemporary Mathematics, vol. 76, American Mathematical Society, Providence, RI, 1988.

    Google Scholar 

  20. Hutchinson, G. andCzédli, G.,A test for identities satisfied in lattices of submodules, Algebra Universalis8 (1978), 269–309.

    Google Scholar 

  21. Jónsson, B.,Modular lattices and Desargues theorem, Math. Scand.2 (1954), 295–314.

    Google Scholar 

  22. Jónsson, B.,Algebras whose congruence lattices are distributive, Math. Scand.21 (1967), 110–121.

    Google Scholar 

  23. Jónsson, B.,Identities in congruence varieties, Lattice theory (Proc. Colloq., Szeged, 1974), Colloq. Math. Soc. János Bolyai, vol. 14, 1976, 195–205.

    Google Scholar 

  24. Jónsson, B.,Congruence Varieties, Algebra Universalis10 (1980), 355–394.

    Google Scholar 

  25. Jónsson, B. andRival, I.,Lattice varieties covering the smallest non-modular variety, Pacific J. Math.82 (1979), 463–478.

    Google Scholar 

  26. Lipparini, Paolo,n-permutable varieties satisfy nontrivial congruence identities, Algebra Universalis33 (1995), 159–168.

    Google Scholar 

  27. Maltsev, A. I.,On the general theory of algebraic systems, (Russian), Mat. Sbornik77 (1954), 3–20.

    Google Scholar 

  28. McKenzie, R.,Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc.174 (1972), 1–43.

    Google Scholar 

  29. McKenzie, R.,Some unsolved problems between lattice theory and equational logic, In Proc. Univ. Houston Lattice Theory Conf., 1973, 563–573.

  30. McKenzie, R., McNulty, G. andTaylor, W.,Algebras, Lattices, Varieties, Volume I, Wadsworth and Brooks/Cole, Monterey, California, 1987.

    Google Scholar 

  31. Mederly, P.,Three Mal'cev type theorems and their applications, Math. Časopis Sloven. Akad. Vied.25 (1975), 83–95.

    Google Scholar 

  32. Nation, J. B.,Congruence lattices of relatively free unary algebras, Algebra Universalis4 (1974), 132.

    Google Scholar 

  33. Nation, J. B.,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis4 (1974), 78–88.

    Google Scholar 

  34. Pálfy, P. P. andSzabó, C.,An identity for subgroup lattices of abelian groups, Algebra Universalis33 (1995), 191–195.

    Google Scholar 

  35. Pixley, A. F.,Distributivity and permutability of congruence relations in equational classes of algebras, Proc. Amer. Math. Soc.14 (1963), 105–109.

    Google Scholar 

  36. Pixley, A. F.,Local Mal'cev conditions, Canad. Math. Bull.15 (1972), 559–568.

    Google Scholar 

  37. Polin, S. V.,Identities in congruence lattices of universal algebras, Mat. Zametki22 (1977), 443–451; English transl, in Mathematical Notes22 (1977), 737–742.

    Google Scholar 

  38. Taylor, W.,Characterizing Mal'cev conditions, Algebra Universalis3 (1973), 351–397.

    Google Scholar 

  39. Wille, R.,Kongruenzklassengeometrien, Lecture Notes in Mathematics, vol.113, Springer-Verlag, New York, 1970.

    Google Scholar 

Download references

Author information

Authors and Affiliations

Authors

Additional information

This research was partially supported by NSF grant no. DMS-9204481. The author would like to thank the referee for several helpful suggestions.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Freese, R. Alan Day's early work: congruence identities. Algebra Universalis 34, 4–23 (1995). https://doi.org/10.1007/BF01200487

Download citation

  • Received:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01200487

Keywords

Navigation