# 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

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topKlaus 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

top- [1] P. Baltazar, M-Solid Varieties of Languages, Acta Cybernetica 18 (2008) 719-731. Zbl1164.68022
- [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. Zbl1170.08002
- [4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2005. Zbl1094.08001
- [5] H. Lugowski, Grundzüge der Universellen Algebra, Teubner-Verlag, Leipzig 1976.

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