Abstract
There is an infinite subdirectly irreducible lattice which generates a variety that contains only finitely many subvarietes.
Similar content being viewed by others
References
Adams, M. E., Freese, R., Nation, J. B. and Schmid, J. (1995) Maximal Sublattices and Frattini Sublattices of Bounded Lattices, preprint.
DayA. and NationJ. B. (1992) Congruence normal covers of finitely generated lattice varieties, Canad. Math. Bull. 35, 311–320.
Freese, R. (1977) The structure of modular lattices of width four with applications to varieties of lattices, Memoirs Amer. Math. Soc. 181.
GrätzerG. (1966) Equational classes of lattices, Duke J. Math. 33, 613–622.
HongD. X. (1972) Covering relations among lattice varieties, Pacific J. Math. 40, 575–603.
JónssonB. (1968) Equational classes of lattices, Math. Scand. 22, 187–196.
JónssonB. and RivalI. (1979) Lattice varieties covering the smallest non-modular variety, Pacific J. Math. 82, 463–478.
LeeJ. G. (1985) Almost distributive lattice varieties, algebra Universalis 21, 280–304.
McKenzieR. (1972) Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc. 174, 1–43.
NationJ. B. (1985) Some varieties of semidistributive lattices, in S.Comer (ed.), Universal Algebra and Lattice Theory, Springer-Verlag, New York, Lecture Notes in Math. 1149, 198–223.
NationJ. B. (1986) Lattice varieties covering V(L 1), Algebra Universalis 23, 132–166.
NationJ. B. (1990) An approach to lattice varieties of finite height, Algebra Universalis 27, 521–543.
Rose, H. (1984) Nonmodular lattice varieties, Memoirs Amer. Math. Soc. 292.
Ruckelshausen, W. (1983) Zur Hierarchie kleiner Verbandsvarietäten,Studentenwerk Darmstadt, Darmstadt, Dissertation.
Wong, C. Y. (1989) Lattice varieties with weak distributivity, Univ. of Hawaii, Honolulu, Ph.D. Thesis.
Author information
Authors and Affiliations
Additional information
Communicated by I. Rival
The author was supported in part by NSF Grant DMS 94-00511
Rights and permissions
About this article
Cite this article
Nation, J.B. A counterexample to the finite height conjecture. Order 13, 1–9 (1996). https://doi.org/10.1007/BF00383963
Received:
Accepted:
Issue Date:
DOI: https://doi.org/10.1007/BF00383963