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Nd-solid varieties

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A non-deterministic hypersubstitution maps any operation symbol of a tree language of type τ to a set of trees of the same type, i.e. to a tree language. Non-deterministic hypersubstitutions can be extended to mappings which map tree languages to tree languages preserving the arities. We define the application of a non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras. Non-deterministic hypersubstitutions can also be applied to equations of type τ. Formally, we obtain two closure operators which turn out to form a conjugate pair of completely additive closure operators. This allows us to use the theory of conjugate pairs of additive closure operators for a characterization of M-solid non-deterministic varieties of algebras. As an application we consider M-solid non-deterministic varieties of semigroups.
Twórcy
  • Universität Potsdam, Fachbereich Mathematik, Postfach 601553, 14415 Potsdam, Germany
  • Chiangmai University, Department of Mathematics, Chiangmai, Thailand 50200
Bibliografia
  • [1] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman & Hall/CRC, Boca Raton, London, New York, Washington, D.C. 2002.
  • [2] K. Denecke, P. Glubudom and J. Koppitz, Power Clones and Non-Deterministic Hypersubstitutions, preprint 2005.
  • [3] F. Gécseg and M. Steinby, Tree Languages, pp. 1-68 in: Handbook of Formal Languages, Vol. 3, Chapter 1, Tree Languages, Springer-Verlag 1997.
  • [4] K. Denecke and J. Koppitz, M-solid Varieties of Algebras, Advances in Mathematics, Vol. 10, Springer 2006.
  • [5] S. Leeratanavalee, Weak hypersubstitutions, Thesis, University of Potsdam 2002.
  • [6] K. Menger, The algebra of functions: past, present, future, Rend. Mat. 20 (1961), 409-430.
  • [7] B.M. Schein, and V.S. Trokhimenko, Algebras of multiplace functions, Semigroup Forum 17 (1979), 1-64.
  • [8] W. Taylor, Abstract Clone Theory, Algebras and Orders, Kluwer Academic Publishers, Dordrecht, Boston, London (1993), 507-530.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1129
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