Abstract
In some recent papers, the concept of a Q-independent sequence of finite lattices was utilized. We investigate this concept in universal algebras and apply it to positive universal classes in locally finite varieties, with emphasis on semilattices, lattices, and their expansions.
Similar content being viewed by others
References
Baker, K.: Personal communication to G. Grätzer, April 5, 2008
Ball R.N.: Distinguished extension of a lattice ordered group. Algebra Universalis 35, 85–112 (1996)
Ball R.N.: Completions of ℓ-groups. In: Glass, A. M.W., Holland, W.C. (eds) Lattice Ordered Groups., pp. 142–174. Kluwer, Dortrect-Boston-London (1989)
Chang C.C., Keisler H.J.: Model Theory. North-Holland, New York (1973)
Czédli, G., Maróti, M.: Two notes on the variety generated by planar modular lattices. To appear in Order
Freese, R.: The structure of modular lattices of width four with applications to varieties of lattices. Memoirs of the AMS 181 (1977)
Grätzer, G.: Lattice Theory: First Concepts and Distributive Lattices. W. H. Freeman and Co., San Fransisco, Calif. (1971). Softcover edition, Dover Publications (2008)
Grätzer, G.: General Lattice Theory, second edition. New appendices by the author with B. A. Davey, R. Freese, B. Ganter, M. Greferath, P. Jipsen, H. A. Priestley, H. Rose, E.T. Schmidt, S. E. Schmidt, F. Wehrung, and R. Wille. Birkhäuser Verlag, Base (1998). Softcover edition, Birkhäuser Verlag, Basel–Boston–Berlin (2003), reprinted, March, 2007
Grätzer, G.: The Congruences of a Finite Lattice, A Proof-by-Picture Approach. Birkhäuser Boston (2006) The Glossary of Notation is available as a pdf file at http://mirror.ctan.org/info/examples/Math_into_LaTeX-4/notation.pdf
Grätzer G., Lakser H.: Subdirectly irreducible modular lattices of width at most 4. Acta Sci. Math. (Szeged) 73, 3–30 (2007)
Grätzer G., Quackenbush R.W.: The variety generated by planar modular lattices. Algebra Universalis 63, 187–202 (2010)
Jónsson B.: Algebras whose congruence lattices are distributive. Math. Scand. 21, 110–121 (1967)
Author information
Authors and Affiliations
Corresponding author
Additional information
Presented by B. Davey.
Rights and permissions
About this article
Cite this article
Grätzer, G., Quackenbush, R.W. Positive universal classes in locally finite varieties. Algebra Univers. 64, 1–13 (2010). https://doi.org/10.1007/s00012-010-0089-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s00012-010-0089-9