Hyperidentities in many-sorted algebras

• Autorzy: Klaus Denecke , Somsak Lekkoksung
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hypersubstitution; hyperidentity; heterogeneous algebra

Kategorie tematyczne

• 08B15: Lattices of varieties
• 08A68: Heterogeneous algebras

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2009
• Tom: 29
• Numer: 1
• Strony: 47-74

Daty

wydano

2009

otrzymano

2009-05-20

poprawiono

2009-09-10

Twórcy

autor

Klaus Denecke

• Universität Potsdam, Institut of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Somsak Lekkoksung

• 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.

Identyfikatory

DOI

10.7151/dmgaa.1151