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A variety generated by a finite algebra with 2x 0 subvarieties

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Abstract

As was indicated to me by Prof. A. Wroński, the following problem was suggested by Prof. B. Jónsson: is every subvariety of the variety of a finite algebra generated by a finite algebra? In this paper we solve this problem in the negative by constructing a finite algebra that generates a variety having 2x 0 subvarieties.

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References

  1. G. Grätzer,Universal algebra, Van Nostrand, Princeton 1968.

    MATH  Google Scholar 

  2. B. Jónsson,Algebras whose congruence lattice are distributive, Math. Scand.21 (1967), 110–121.

    MATH  MathSciNet  Google Scholar 

  3. R. C. Lyndon,Identities in finite algebras, Proc. Amer. math. Soc.71 (1951), 457–465.

    MATH  MathSciNet  Google Scholar 

  4. V. L. Murskiî,The existence in the three-valued logic of a closed class with a finite basis having no finite complete system of identities, Dokl. Acad. Nauk SSSR,163, (1965), 815–818 (in Russian)=Soviet. Mathematics Doklady,6 (1965), 1020–1024 (in English).

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Dziobiak, W. A variety generated by a finite algebra with 2x 0 subvarieties. Algebra Universalis 13, 148–156 (1981). https://doi.org/10.1007/BF02483829

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  • DOI: https://doi.org/10.1007/BF02483829

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