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Skew Boolean algebras and discriminator varieties

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Abstract

We investigate the class of skew Boolean algebras which are also meet semilattices under the natural skew lattice partial order. Such algebras, called hereskew Boolean ∩-algebras, are quite common. Indeed, any algebra A in a discriminator variety with a constant term has a skew Boolean ∩-algebra polynomial reduct whose congruences coincide with those of A.

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References

  1. Bignall, R. J.,A non-commutative multiple-valued logic, Proceedings of the Twenty First International Symposium on Multiple-Valued Logic, IEEE Computer Society Press, (1991), 49–54.

  2. Burris, S. andSankappanavar, H. P.,A Course in Universal Algebra, Springer-Verlag, New York (1981).

    Google Scholar 

  3. Cornish, W. H.,Boolean skew algebras, Acta Math. Acad. Sci. Hung.36 (1980), 281–291.

    Google Scholar 

  4. Cornish, W. H.,On Iséki's BCK-algebras, in: P. Schultz, C. Praeger, R. Sullivan (eds),Algebraic Structures and Applications, Lecture Notes in Pure and Applied Mathematics, Marcel Dekker, Vol. 74 (1982), 101–122.

  5. Davey, B. A., Schumann, V. J. andWerner, H.,From the subalgebras of the square to the discriminator, Algebra Universalis28 (1991), 500–519.

    Google Scholar 

  6. Iséki, K. andTanaka, S.,An introduction to the theory of BCK-algebras, Math. Japonica23 (1978), 1–26.

    Google Scholar 

  7. Keimel, K. andWerner, H.,Stone duality for varieties generated by quasi-primal algebras, Memoirs of the American Mathematical Society148 (1974), 59–85.

    Google Scholar 

  8. Leech, J.,Skew lattices in rings, Algebra Universalis26 (1989), 48–72.

    Google Scholar 

  9. Leech, J.,Skew Boolean algebras, Algebra Universalis27 (1990), 497–506.

    Google Scholar 

  10. Leech, J.,Normal skew lattices, Semigroup Forum44 (1992), 1–8.

    Google Scholar 

  11. Leech, J.,The geometric structure of skew lattices, Transactions of the American Mathematical Society335 (1993), 823–842.

    Google Scholar 

  12. McKenzie, R.,On spectra, and the negative solution of the decision problem for algebras having a finite non-trivial model, Jour. Symb. Logic40 (1975), 186–195.

    Google Scholar 

  13. Murskii, V. L.,The existence of a finite basis, and some other properties, for “almost all” finite algebras (Russian), Problemy Kilbernet.50 (1975), 43–56.

    Google Scholar 

  14. Muzio, J. C. andWesselkamper, T. C.,Multiple-Valued Switching Theory, Adam Hilger, Bristol (1986).

    Google Scholar 

  15. Yutani, H.,On a system of axioms of a commutative BCK algebra, Math. Sem. Notes5 (1977), 255–256.

    Google Scholar 

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Authors and Affiliations

  1. Gippsland School of Computing and Information Technology, Monash University Gippsland Campus, 3842, Churchill, Victoria, Australia

    R. J. Bignall & J. E. Leech

  2. Department of Mathematics and Computer Science, Westmont College, 93108-1099, Santa Barbara, California, USA

    R. J. Bignall & J. E. Leech

Authors
  1. R. J. Bignall
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  2. J. E. Leech
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Bignall, R.J., Leech, J.E. Skew Boolean algebras and discriminator varieties. Algebra Universalis 33, 387–398 (1995). https://doi.org/10.1007/BF01190707

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  • DOI: https://doi.org/10.1007/BF01190707

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