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The unique minimal clone with three essentially binary operations

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References

  1. Belousov, W.,Foundations of the theory of quasigroups and loops. Moscow, 1967 (in Russian).

  2. Blochina, C. N.,On predicate description of Post classes (Russian). Diskret. Analiz16 (1970), 16–29.

    Google Scholar 

  3. Csákány, B.,Varieties of affine modules. Acta Sci. Math. (Szeged)37 (1975), 3–10.

    Google Scholar 

  4. Csákány, B.,On affine spaces over prime fields. Acta Sci. Math. (Szeged)37(1975), 33–36.

    Google Scholar 

  5. Csákány, B.,All minimal clones on the three-element set. Acta Cybernetica6 (1983), 227–238.

    Google Scholar 

  6. Dudek, J.,Varieties of idempolent commutative groupoids. Fund. Math.,120(1984), 193–204.

    Google Scholar 

  7. Dudek, J.,On binary polynomials in idempotent commutative groupoids. Fund. Math.120 (1984), 187–191.

    Google Scholar 

  8. Dudek, J.,On the minimal extension of sequences. Algebra Universalis23 (1986), 308–312.

    Google Scholar 

  9. Grätzer, G.,Universal Algebra. Springer-Verlag, Berlin-Heidelberg-New York, 1979.

    Google Scholar 

  10. Grätzer, G. andPadmanabhan, R.,On idempotent commutative and non-associative groupoids. Proc. Amer. Math. Soc.28 (1971), 75–80.

    Google Scholar 

  11. Machida, H.,Essentially minimal closed sets in multiple-valued logic. Trans. IECE Japan,E64 (4) (1981) 243–245.

    Google Scholar 

  12. Machida, H. andRosenberg, I. G.,Classifying essentially minimal clones, in:Proceeding 14th Intern. Sympos. Multiple-valued Logics. Winnipeg, 1984 (IEFE), pp. 4–7.

  13. Pálfy, P. P.,The arity of minimal clones. Acta Sci. Math.50 (1986), 331–333.

    Google Scholar 

  14. Park, R. E.,A four-element algebra whose identities are not finitely based. Algebra Universalis11 (1980), 225–260.

    Google Scholar 

  15. Płonka, J.,On the arity of idempotent reduct of groups. Colloq. Math.21 (1970), 35–37.

    Google Scholar 

  16. Płonka, J.,R-prime idempotent reducts of groups. Archiv der Math.24 (1973), 129–132.

    Google Scholar 

  17. Post, E.,The two-valued iterative systems of mathematical logics. Annals of Math. Studies No. 5. Princeton University Press, Princeton, NJ, 1941.

    Google Scholar 

  18. Rosenberg, I. G.,Minimal clones I, The five types, in: L. Szabó and A. Szendrei (eds.)Lectures in Universal Algebra. Colloq. Math. Soc. J. Bolyai 43. North-Holland, Amsterdam, 1986, pp. 405–427.

    Google Scholar 

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Dudek, J. The unique minimal clone with three essentially binary operations. Algebra Universalis 27, 261–269 (1990). https://doi.org/10.1007/BF01182459

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