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Abstrakty
The theory of hyperidentities generalizes the equational theory of universal algebras and is applicable in several fields of science, especially in computers sciences (see e.g. [2,1]). The main tool to study hyperidentities is the concept of a hypersubstitution. Hypersubstitutions of many-sorted algebras were studied in [3]. On the basis of hypersubstitutions one defines a pair of closure operators which turns out to be a conjugate pair. The theory of conjugate pairs of additive closure operators can be applied to characterize solid varieties, i.e., varieties in which every identity is satisfied as a hyperidentity (see [4]). The aim of this paper is to apply the theory of conjugate pairs of additive closure operators to many-sorted algebras.
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Tom
Numer
Strony
47-74
Opis fizyczny
Daty
wydano
2009
otrzymano
2009-05-20
poprawiono
2009-09-10
Twórcy
autor
- Universität Potsdam, Institut of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
autor
- Universität Potsdam, Institut of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
Bibliografia
- [1] P. Baltazar, M-Solid Varieties of Languages, Acta Cybernetica 18 (2008) 719-731.
- [2] K. Denecke and S. L. Wismath, Hyperidenties and Clones, Gordon and Breach, 2000.
- [3] K. Denecke and S. Lekkoksung, Hypersubstitutions of Many-Sorted Algebras, Asian-European J. Math. Vol. I (3) (2008) 337-346.
- [4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2005.
- [5] H. Lugowski, Grundzüge der Universellen Algebra, Teubner-Verlag, Leipzig 1976.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1151