References
Adams, M. E.,Uniquely complemented lattices, The Dilworth Theorems, Selected Papers of Robert P. Dilworth (K. Bogart, R. Freese, and J. Kung, eds.), Birkhäuser, Basel, 1990, pp. 79–84.
Birkhoff, G.,On the structure of abstract algebras, Proc. Cambridge Phil. Soc.31 (1935), 433–454.
Crawley, P. andDilworth, R. P.,Algebraic Theory of Lattices, Prentice-Hall, Englewood Cliffs, New Jersey, 1973.
Czedli, G. andFreese, R.,On congruence distributivity and modularity, Algebra Universalis17 (1983), 216–219.
Day, A.,p-modularity implies modularity in equational classes, Algebra Universalis3 (1973), 398–399.
Day, A.,Lattice conditions implying congruence modularity, Algebra Universalis6 (1976), 291–301.
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, pp. 57–71.
Day, A. andFreese, R.,A characterization of identities implying congruence modularity, I, Cand. J. Math.52 (1980), 1140–1167.
Day, A.,Herrmann, C,Jónsson, B.,Nation, J. B. andPickering, D.,Minimal non-Arguesian lattices, Algebra Universalis, to appear.
Day, A. andJežek, J.,The amalgamation property for varieties of lattices, Trans. Amer. Math. Soc.286 (1984), 251–256.
Day, A. andJónsson, B.,The structure of non-Arguesian lattices, Bull. Amer. Math. Soc.13 (1985), 157–159.
Day, A. andJónsson, B.,A structural characterization of non-Arguesian lattices, Order2 (1986), 335–350.
Day, A. andJónsson, B.,Non-Arguesian configurations in a modular lattice, Acta Sci. Math. (Szeged)51 (1987), 309–318.
Day, A. andJónsson, B.,Non-Arguesian configurations and gluings of modular lattices, Algebra Universalis26 (1989), 208–215.
Dedekind, R.,Über Zerlegungen von Zahlen durch ihre grössten gemeinsamen Teiler, Festschrift der Herzogl. technische Hochschule zur Naturforscher-Versammlung, Braunschweig (1897), Reprinted in “Gesammelte mathematische Werke”, Vol. 2, pp. 103–148, Chelsea, New York, 1968.
Dedekind, R.,Über die drei Moduln erzengte Dualgruppe, Math. Annalen53 (1900), 371–403.
Dilworth, R. P.,Lattices with unique complements, Trans. Amer. Math. Soc.57 (1945), 123–154.
Dilworth, R. P.,The structure of relatively complemented lattices, Ann. of Math.51 (1950), 348–359.
Freese, R.,The variety of modular lattices is not generated by its finite members, Trans. Amer. Math. Soc.255 (1979), 277–300.
Freese, R.,Free modular lattices, Trans. Amer. Math. Soc.261 (1980), 81–91.
Freese, R.,Connected components of the covering relation in free lattices, Universal Algebra and Lattice Theory, S. Comer, ed., Lecture Notes in Mathematics, vol. 1149, Springer-Verlag, New York, 1985, pp. 82–93.
Freese, R.,Finitely presented lattices: canonical forms and the covering relation, Trans. Amer. Math. Soc.312 (1989), 841–860.
Freese, R.,Modular congruence varieties, Algebra Universalis, to appear.
Freese, R., Herrmann, C. andHuhn, A. P.,On some identities valid in modular congruence varieties, Algebra Universalis12 (1981), 322–334.
Freese, R. andJónsson, B.,Congruence modularity implies the Arguesian identity, Algebra Universalis6 (1976), 225–228.
Freese, R. andNation, J. B., 3-3lattice inclusions imply congruence modularity, Algebra Universalis7 (1977), 191–194.
Freese, R. andNation, J. B.,Protective lattices, Pacific J. Math.75 (1978), 93–106.
Freese, R. andNation, J. B.,Covers in free lattices, Trans. Amer. Math. Soc.288 (1985), 1–42.
Galvin, F. andJónsson, B.,Distributive sublaltices of a free lattice, Canadian J. Math.13 (1961), 265–272.
Gedeonová, E.,A characterization of p-modularity for congruence lattices of algebras, Acta. Fac. Rerum Natur. Univ. Comenian. Math. Publ.28 (1972), 99–106.
Grätzer, G., Jónsson, B. andLakser, H.,The amalgamation property in equational classes of modular lattices, Pacific J. Math.45 (1973), 507–524.
Grätzer, G. andPlatt, C. R.,A characterization of sharply transferable lattices, Canad. J. Math.52 (1980), 145–154.
Haiman, M.,Arguesian lattices which are not linear, Bull. Amer. Math. Soc.16 (1987), 121–124.
Haiman, M.,Arguesian lattices which are not type-1, Algebra Universalis28 (1991), 128–137.
Herrmann, Ch.,On the word problem for modular lattices with four generators, Math. Ann.265 (1983), 513–527.
Herrmann, Ch.,On the arithmetic of projective coordinate systems, Trans. Amer. Math. Soc.284 (1984), 759–785.
Hobby, D. andMcKenzie, R.,The Structure of Finite Algebras (tame congruence theory), Contemporary Mathematics, American Mathematical Society, Providence, RI, 1988.
Jónsson, B.,On the representation of lattices, Math. Scand.1 (1953), 193–206.
Jónsson, B.,Modular lattices and Desargues theorem, Math. Scand.2 (1954), 295–314.
Jónsson, B.,Representations of complemented modular lattices, Trans. Amer. Math. Soc.97 (1960), 64–94.
Jónsson, B.,Sublattices of a free lattice, Canad. J. Math.13 (1961), 256–264.
Jónsson, B.,Varieties of algebras and their congruence varieties, Proc. Int. Congr. of Math., Vancouver, B.C., 1974, Canadian Math. Congress, 1975, pp. 315–320.
Jónsson, B.,Identities in congruence varieties, Lattice theory (Proc. Colloq., Szeged, 1974), Colloq. Math. Soc. János Bolyai, vol. 14, 1976, pp. 195–205.
Jónsson, B.,Varieties of lattices: Some open problems, Universal Algebra, Colloq. Math. Soc. János Bolyai vol. 29, 1982, pp. 421–436.
Jónsson, B. andNation, J. B.,A report on sublattices of a free lattice, Coll. Math. Soc. János Bolyai17 (1977), 233–257.
Kostinsky, A.,Projective lattices and bounded homomorphisms, Pacific J. Math.40 (1972), 111–119.
McKenzie, R.,Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc.174 (1972), 1–43.
McKenzie, R., McNulty, G. andTaylor, W.,Algebras, Lattices, Varieties, Volume I, Wadsworth and Brooks/Cole, Monterey, California, 1987.
Mederly, P.,Three Mal'cev type theorems and their applications, Math. Časopis Sloven. Akad. Vied.25 (1975), 83–95.
Nation, J. B.,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis4 (1974), 78–88.
Nation, J. B.,Bounded finite lattices, Universal Algebra, Colloq. Math. Soc. János Bolyai vol. 29, 1982, pp. 531–533.
Nation, J. B.,Finite sublattices of a free lattice, Trans. Amer. Math. Soc.269 (1982), 311–337.
Nation, J. B.,Jónsson's contributions to lattice theory, this volume.
Ore, O.,Theory of equivalence relations, Duke Math. J.9 (1942), 573–627.
Pickering, D.,Minimal non-Arguesian lattices, Ph.D. Thesis, University of Hawaii, 1984.
Polin, S. V.,Identities in congruence lattices of universal algebras, (Russian), Mat. Zametki22 (1977), 443–451.
Tschantz, S. T.,Infinite intervals in free lattices, Order6 (1990), 367–388.
Whitman, Ph. M.,Free lattices II, Ann. of Math. (2)43 (1942), 104–115.
Author information
Authors and Affiliations
Additional information
Dedicated to Bjarni Jónsson on his 70th birthday
The research for this paper was partially supported by NSF grant no. DMS89-01756. It is loosely based on a talk given at the Jönsson Symposium, Laugarvatn, Iceland, July 2–6, 1990.
Rights and permissions
About this article
Cite this article
Freese, R. Directions in lattice theory. Algebra Universalis 31, 416–429 (1994). https://doi.org/10.1007/BF01221796
Issue Date:
DOI: https://doi.org/10.1007/BF01221796