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Abstract

The previous sections have included various algorithms for working with locally finite quasivarieties of finite type. We will illustrate these algorithms by applying them to quasivarieties contained in the variety \(\mathcal{M}\) generated by a particular 3-element algebra M described below.

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Bibliography

  1. M.E. Adams, W. Dziobiak, Q-universal quasivarieties of algebras. Proc. Am. Math. Soc. 120, 1053–1059 (1994)

    MathSciNet  MATH  Google Scholar 

  2. M.E. Adams, W. Dziobiak, Lattices of quasivarieties of 3-element algebras. J. Algebra 166, 181–210 (1994)

    Article  MathSciNet  Google Scholar 

  3. M.E. Adams, W. Dziobiak, Quasivarieties of distributive lattices with a quantifier. Discrete Math. 135, 15–28 (1994)

    Article  MathSciNet  Google Scholar 

  4. M.E. Adams, W. Dziobiak, The lattice of quasivarieties of undirected graphs. Algebra Univers. 47, 7–11 (2002)

    Article  MathSciNet  Google Scholar 

  5. M.E. Adams, W. Dziobiak, Quasivarieties of idempotent semigroups. Int. J. Algebra Comput. 13, 733–752 (2003)

    Article  MathSciNet  Google Scholar 

  6. M.E. Adams, W. Dziobiak, Universal quasivarieties of algebras, in Proceedings of the 9th “Dr. Antonio A. R. Monteiro” Congress, Actas Cong. “Dr. Antonio A. R. Monteiro” (Univ. Nac. del Sur, Baía Blanca, 2008), pp. 11–21

    Google Scholar 

  7. M.E. Adams, W. Dziobiak, M. Gould, J. Schmid, Quasivarieties of pseudocomplemented semilattices. Fund. Math. 146, 295–312 (1995)

    MathSciNet  MATH  Google Scholar 

  8. G. Birkhoff, On the structure of abstract algebras. Proc. Camb. Philos. Soc. 31, 432–454 (1935)

    Article  Google Scholar 

  9. D. Casperson, J. Hyndman, J. Mason, J. Nation, B. Schaan, Existence of finite bases for quasi-equations of unary algebras with 0. Int. J. Algebra Comput. 25, 927–950 (2015)

    Article  MathSciNet  Google Scholar 

  10. A.V. Kravchenko, Q-universal quasivarieties of graphs. Algebra Logic 41, 173–181 (2002)

    Article  MathSciNet  Google Scholar 

  11. A. Nurakunov, Lattices of quasivarieties of pointed abelian groups. Algebra Logic 53, 238–257 (2014)

    Article  MathSciNet  Google Scholar 

  12. M. Sapir, The lattice of quasivarieties of semigroups. Algebra Univers. 21, 172–180 (1985)

    Article  MathSciNet  Google Scholar 

  13. M. Sheremet, Quasivarieties of Cantor algebras. Algebra Univers. 46, 193–201 (2001)

    Article  MathSciNet  Google Scholar 

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Hyndman, J., Nation, J.B. (2018). Unary Algebras with 2-Element Range. In: The Lattice of Subquasivarieties of a Locally Finite Quasivariety. CMS Books in Mathematics. Springer, Cham. https://doi.org/10.1007/978-3-319-78235-5_5

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