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In 2009 K.Denecke and J.Koppitz proved that for a monoid M of hypersubstitutions M-solid positive varieties of tree languages correspond to M-solid ordered pseudovarieties. In this paper, we will characterize M-solid ordered pseudovarieties in a similar way in which in [14] M-solid varieties, in [3] M-solid quasivarieties, in [11] M-solid pseudovarieties and in [12] M-solid algebraic systems were characterized. The main idea is to show, that we have two Galois-connections and a conjugate pair of additive closure operators. Then we can apply the general theory of conjugate pairs of additive closure operators.
Wydawca
Czasopismo
Rocznik
Tom
Strony
723--738
Opis fizyczny
Bibliogr. 17 poz.
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autor
autor
- Mathematics Institute Potsdam University Am Neuen Palais 14415 Potsdam, Germany, kdenecke@rz.uni-potsdam.de
Bibliografia
- [1] A. I. Mal’cev, Algebraic Systems, Akademie-Verlag, Berlin 1973.
- [2] B. Pibaljommee, M-solid pseudovarieties, Ph. D. thesis, Potsdam 2004.
- [3] Ch. Chompoonut, K. Denecke, M-solid quasivarieties, East-West J. Math. 4(2) (2002), 177–190.
- [4] E. Graczyńska, D. Schweigert, Hyperidentities of a given type, Algebra Universalis 27 (1990), 305–318.
- [5] E. Graczyńska, R. Pöschel, M. V. Volkov, Solid pseudovarieties, General Algebra and Applications in Discrete Mathematics, Proceedings of the conference on General Algebra and Discrete Mathematics, Potsdam 1996, pp. 93–110.
- [6] J.-E. Pin, P. Well, A Reiterman theorem for pseudovarieties of finite first-order structures, Algebra Universalis 35 (1996), 577–595.
- [7] J. Koppitz, K. Denecke, M-solid Varieties, Springer 2006.
- [8] J. Reiterman, The Birkhoff theorem for finite algebras, Algebra Universalis 14 (1982), 1–10.
- [9] K. Denecke, J. Koppitz, M-solid positive varieties of tree languages, preprint 2009.
- [10] K. Denecke, D. Lau, R. Pöschel, D. Schweigert, Hyperidentities, hyperequational classes, and clone congruences, Contributions to General Algebra 7, Verlag Hölder-Pichler-Tempsky, Wien 1991, 97–118.
- [11] K. Denecke, B. Pibaljommee, Pseudoidentities and hyper-pseudoidentities, Advances in Algebra towards Millenium Problems, ed. by Ki-Bong Nam et. al., SAS International Publications, 2005, pp. 163–180.
- [12] K. Denecke, D. Phusanga, Hyperformulas and solid algebraic systems, Studia Logica 90(2) (2008), 263–286.
- [13] K. Denecke, D. Phusanga, Hypersatisfaction of formulas in algebraic systems, Discuss. Math. Gen. Algebra Appl. 29(2) (2009), 123–153.
- [14] K. Denecke, M. Reichel, Monoids of hypersubstitutions and M-solid varieties, Contributions to General Algebra 9, Verlag Hölder-Pichler- Temsky, Wien 1995, Verlag B. G. Teubner, Stuttgart, pp. 117–126.
- [15] K. Denecke, S. L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers, 2000.
- [16] K. Denecke, S. L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Chapman and Hall/CRC, 2002.
- [17] P. Baltazar, M-solid varieties of languages, Acta Cybernet. 18 (2008), 719–731.
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Bibliografia
Identyfikator YADDA
bwmeta1.element.baztech-article-PWA4-0033-0027