Keywords
- Lattice Variety
- Homomorphic Image
- Universal Algebra
- Irreducible Element
- Finite Lattice
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, access via your institution.
Buying options
Tax calculation will be finalised at checkout
Purchases are for personal use only
Learn about institutional subscriptionsPreview
Unable to display preview. Download preview PDF.
References
Berman, J. and Wolk, B., Free lattices in some small varieties, Algebra Universalis, 10(1980), 269–289.
Birkhoff, G., On the lattice theory of ideals, Bull. Amer. Math. Soc., 40(1934), 613–619.
Birkhoff, G., Lattice Theory, 3rd ed. (1967), Providence, R.I., American Mathematical Society.
Day, A., A simple solution to the word problem for lattices, Canadian Math. Bull., 13(1970), 253–254.
Day, A., Splitting lattices generate all lattices, Algebra Universalis, 7(1977), 163–169.
Day, A., Characterizations of lattices that are bounded-homomorphic images or sublattices of free lattices, Canadian J. Math., 31(1979), 69–78.
Day, A. and Nation, J.B., A note on finite sublattice of free lattices, Algebra Universalis, 15(1982), 90–94.
Dedekind, R., Über die von drei Moduln erzeugte Dualgruppe, Math. Ann., 53(1900), 371–403.
Freese, R., Ideal lattices of lattices, Pacific J. Math., 57(1975), 125–133.
Freese, R., The structure of modular lattices of width four with applications to varieties of lattices, Memoirs Amer. Math. Soc., no. 181 (1977), Providence, R.I., American Mathematical Society.
Freese, R. and Nation, J. B., Covers in free lattices, to appear in Trans. Amer. Math. Soc.
Grätzer, G., Equational classes of lattices, Duke Math. J., 33(1966), 613–622.
Hong, D. X., Covering relations among lattice varieties, Pacific J. Math., 40(1972), 575–603.
Jónsson, B., Algebras whose congruence lattices are distributive, Math. Scand., 21(1967), 110–121.
Jónsson, B., Equational classes of lattices, Math. Scand., 22(1968), 187–196.
Jónsson, B., Varieties of lattices: some open problems, Coll. Math. Soc. János Bolyai, 29(1982), Contributions to Universal Algebra (Esztergom), North Holland, 421–436.
Jónsson, B. and Nation, J. B., A report on sublattices of a free lattice, Coll. Math. Soc. János Bolyai, 17(1977), Contributions to Universal Algebra (Szeged), North Holland, 233–257.
Jónsson and Rival, I., Lattice varieties covering the smallest nonmodular variety, Pacific J. Math., 82(1979), 463–478.
Lee. J. G., Almost distributive lattice varieties, Ph.D. Dissertation, Vanderbilt University, 1983.
McKenzie, R., Equational bases and nonmodular lattice varieties, Trans. Amer. Math. Soc., 174(1972), 1–43.
Nation, J. B., Bounded finite lattices, Coll. Math. Soc. János Bolyai, 29(1982), Contributions to Universal Algebra (Esztergom), North Holland, 531–533.
Nation, J. B., Finite sublattices of a free lattice, Trans. Amer. Math. Soc., 269(1982), 311–337.
Rose, H., Nonmodular lattice varieties, Memoris Amer. Math. Soc., no. 292 (1984), Providence, R.I., American Mathematical Society.
Waterman, A. G., The free lattice with 3 generators over N5, Portugal. Math. 26(1967), 285–288.
Author information
Authors and Affiliations
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 1985 Springer-Verlag
About this paper
Cite this paper
Nation, J.B. (1985). Some varieties of semidistributive lattices. In: Comer, S.D. (eds) Universal Algebra and Lattice Theory. Lecture Notes in Mathematics, vol 1149. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0098466
Download citation
DOI: https://doi.org/10.1007/BFb0098466
Published:
Publisher Name: Springer, Berlin, Heidelberg
Print ISBN: 978-3-540-15691-8
Online ISBN: 978-3-540-39638-3
eBook Packages: Springer Book Archive
