Hyperidentities in many-sorted algebras

Klaus Denecke; Somsak Lekkoksung

Discussiones Mathematicae - General Algebra and Applications (2009)

  • Volume: 29, Issue: 1, page 47-74
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Klaus Denecke, and Somsak Lekkoksung. "Hyperidentities in many-sorted algebras." Discussiones Mathematicae - General Algebra and Applications 29.1 (2009): 47-74. <http://eudml.org/doc/276947>.

@article{KlausDenecke2009,
abstract = {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.},
author = {Klaus Denecke, Somsak Lekkoksung},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hypersubstitution; hyperidentity; heterogeneous algebra; many-sorted algebra},
language = {eng},
number = {1},
pages = {47-74},
title = {Hyperidentities in many-sorted algebras},
url = {http://eudml.org/doc/276947},
volume = {29},
year = {2009},
}

TY - JOUR
AU - Klaus Denecke
AU - Somsak Lekkoksung
TI - Hyperidentities in many-sorted algebras
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2009
VL - 29
IS - 1
SP - 47
EP - 74
AB - 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.
LA - eng
KW - hypersubstitution; hyperidentity; heterogeneous algebra; many-sorted algebra
UR - http://eudml.org/doc/276947
ER -

References

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  1. [1] P. Baltazar, M-Solid Varieties of Languages, Acta Cybernetica 18 (2008) 719-731. Zbl1164.68022
  2. [2] K. Denecke and S. L. Wismath, Hyperidenties and Clones, Gordon and Breach, 2000. 
  3. [3] K. Denecke and S. Lekkoksung, Hypersubstitutions of Many-Sorted Algebras, Asian-European J. Math. Vol. I (3) (2008) 337-346. Zbl1170.08002
  4. [4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2005. Zbl1094.08001
  5. [5] H. Lugowski, Grundzüge der Universellen Algebra, Teubner-Verlag, Leipzig 1976. 

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