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2016 | 36 | 1 | 25-43
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M-solid generalized non-deterministic varieties

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EN
Abstrakty
EN
A generalized non-deterministic hypersubstitution is a mapping which maps operation symbols of type τ to the set of terms of the same type which does not necessarily preserve the arity. We apply the generalized non-deterministic hypersubstitution to an algebra of type τ and obtain a class of derived algebras of type τ. The generalized non-deterministic hypersubstitutions can be also applied to sets of equations of type τ. We obtain two closure operators which turn out to be a conjugate pair of completely additive closure operators. This allows us to apply the theory of conjugate pairs of additive closure operators to characterize M-solid generalized non-deterministic varieties of algebras.
Twórcy
  • Department of Mathematics, Faculty of Engineering, Rajamangala University of Technology Isan, Khon Kaen Campus. 40000, Thailand
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 and P. Glubudom, Nd-solid varieties, Discussiones Mathematicae, General Algebra and Applications 27 2007, 245-262. doi: 10.7151/dmgaa
  • [3] K. Denecke, P. Glubudom and J. Koppitz, Power clones and Non-detreministic hypersubstitutions, Asian-European J. Math.1 2008, 177-188. doi: 10.1142/S1793557108000175
  • [4] K. Denecke and J. Koppitz, M-solid varieties of algebras (Advances in Mathematics, Vol. 10, Springer, 2006).
  • [5] E. Graczyńska and D. Schweigert, Hypervarieties of a given tpye, Algebra Universalis 27 1990, 305-318.
  • [6] S. Leeratanavalee and K. Denecke, Generalized Hypersupstitutions and Strongly Solid Varieties, In General Algebra and Applications, Proc. of the '59 th Workshop on General Algebras', '15 th Conference for Young Algebraists Potsdam 2000', Shaker Verlag (2000), 135-145.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1249
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