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Positive universal classes in locally finite varieties

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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.

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References

  1. Baker, K.: Personal communication to G. Grätzer, April 5, 2008

  2. Ball R.N.: Distinguished extension of a lattice ordered group. Algebra Universalis 35, 85–112 (1996)

    Article  MATH  MathSciNet  Google Scholar 

  3. 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)

    Google Scholar 

  4. Chang C.C., Keisler H.J.: Model Theory. North-Holland, New York (1973)

    MATH  Google Scholar 

  5. Czédli, G., Maróti, M.: Two notes on the variety generated by planar modular lattices. To appear in Order

  6. Freese, R.: The structure of modular lattices of width four with applications to varieties of lattices. Memoirs of the AMS 181 (1977)

  7. Grätzer, G.: Lattice Theory: First Concepts and Distributive Lattices. W. H. Freeman and Co., San Fransisco, Calif. (1971). Softcover edition, Dover Publications (2008)

  8. 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

  9. 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

  10. Grätzer G., Lakser H.: Subdirectly irreducible modular lattices of width at most 4. Acta Sci. Math. (Szeged) 73, 3–30 (2007)

    MATH  MathSciNet  Google Scholar 

  11. Grätzer G., Quackenbush R.W.: The variety generated by planar modular lattices. Algebra Universalis 63, 187–202 (2010)

    Article  MATH  Google Scholar 

  12. Jónsson B.: Algebras whose congruence lattices are distributive. Math. Scand. 21, 110–121 (1967)

    MATH  MathSciNet  Google Scholar 

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Correspondence to G. Grätzer.

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Presented by B. Davey.

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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

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  • DOI: https://doi.org/10.1007/s00012-010-0089-9

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