References
Adaricheva, K. V.,A characterization of finite lattices of subsemilattices (in Russian), Algebra i Logica30 (1991), 385–404.
Adaricheva, K. V. andGorbunov, V. A.,The structure of finite atomistic lattices of quasivarieties, Soviet Math. Dokl.41 (1990), 80–82.
Adaricheva, K. V., Dziobiak, W. andGorbunov, V. A.,Finite atomistic lattices that can be represented as lattices of quasivarieties, Fund. Math.142 (1993), 19–43.
Day, A.,A simple solution of the word problem for lattices, Canad. Math. Bull.13 (1970), 253–254.
Day, A.,p-modularity implies modularity in equational classes, Algebra Universalis3 (1973), 398–399.
Day, A.,Splitting lattices generate all lattices, Algebra Universalis7 (1977), 163–170.
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.
Day, A.,Characterizations of finite lattices that are bounded-homomorphic images or sublattices of free lattices, Canad. J. Math.31 (1979), 69–78.
Day, A.,Congruence normality: the characterization of the doubling class of convex sets, Appendix by J. B. Nation, Algebra Universalis31 (1994), 397–406.
Day, A.,Doubling constructions in lattice theory, Canad. J. Math.44 (1992), 252–269.
Day, A. andFreese, R.,A characterization of identities implying congruence modularity, I, Canad. J. Math.32 (1980), 1140–1167.
Day, A. andNation, J. B.,Congruence normal covers of finitely generated lattice varieties, Canad. Math. Bull.35 (1992), 311–320.
Freese, R.,Finitely presented lattices: canonical forms and the covering relation, Trans. Amer. Math. Soc.312 (1989), 841–860.
Freese, R.,Finitely presented lattices: continuity and semidistributivity, Lattices, Semigroups, and Universal Algebra (J. Almeida, G. Bordalo, and Philip Dwinger, eds), Proceedings of the Lisbon Conference, 1988, Plenum Press, New York, 1990, 67–70.
Freese, R.,Free and finitely presented lattices, Proceedings of the International Conference on Algebra honoring A. Maltsev (L. A. Bokut, Yu. L. Ershov, and A. I. Kostríkin, eds.), vosibirsk, USSR, August 21–26, 1989. Contemporary Math., vol.131 (Part 3), 1992, 85–97.
Freese, R.,Weak atomicity in finitely presented lattices: an example, preprint.
Freese, R.,Alan Day's early work: congruence identities, Algebra Universalis34 (1995), 4–23.
Freese, R. andNation, J. B.,3-3 lattice inclusions imply congruence modularity, Algebra Universalis7 (1977), 191–194.
Freese, R., Kearnes, K. andNation, J. B.,Congruence lattices of congruence semidistributive algebras, Proceedings of the Internation Conference Honoring Garrett Birkhoff (K. Baker, E. T. Schmidt and R. Wille, eds.), Darmstadt, Germany, June 13–17, 1991. Springer-Verlag, New York (to appear).
Geyer, W.,The generalized doubling construction and formal concept analysis, Algebra Universalis32 (1994), 341–367.
Geyer, W.,On Tamari lattices, Discrete Math, (to appear).
Gorbunov, V. A.,The structure of lattices of quasivarieties, Algebra Universalis32 (1994), 493–530.
Grãtzer, G.,Chapter on Universal algebra, Trends in lattice theory, edited by J. C. Abbott, Van Nostrand Reinhold, New York (1970).
Grãtzer, G.,A property of transferable lattices, Proc. Amer. Math. Soc.43 (1974), 269–271.
Jónsson, B.,Relatively free lattices, Coll. Math.21 (1970), 191–196.
McKenzle, R.,Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc.174 (1972), 1–43.
Nation, J. B.,Varieties whose congruences satisfy certain lattice identities, Algebra Universalis4 (1974), 78–88.
Nation, J. B.,An approach to lattice varieties of finite height. Algebra Universalis27 (1990), 521–543.
Repnitskii, V. B.,On finite lattices which are emheddable in subsemigroup lattices, preprint (1992).
Repnitskii, V. B.,On sublattices of subsemigroup lattices, preprint (1992).
Skolem, T.,Logisch-kombinatorische Untersuchungen über die Erfüllbarkeit und Beweisbarkeit mathematischen Sätze nebst einem Theoreme über dichte Mengen, Videnskapsselskapets skrifter I. Mathematisk-naturvidenskabelig klasse, Videnskabsakademiet i Kristiania4 (1920), 1–36.
Skolem, T.,Select Works in Logic, Scandinavian University Books, Oslo, 1979.
Slavík, V.,Lattices with finite W-covers, Algebra Universalis (to appear).
Ph. M. Whitman,Free lattices, Ann. of Math. (2)42 (1941), 325–330.
Author information
Authors and Affiliations
Additional information
This work was supported in part by NSF Grant DMS 91-22011.
Rights and permissions
About this article
Cite this article
Nation, J.B. Alan Day's doubling construction. Algebra Universalis 34, 24–34 (1995). https://doi.org/10.1007/BF01200488
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF01200488