Non-Deterministic Linear Hypersubstitutions

Nareupanat Lekkoksung; Prakit Jampachon

Discussiones Mathematicae - General Algebra and Applications (2015)

  • Volume: 35, Issue: 1, page 97-103
  • ISSN: 1509-9415

Abstract

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A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of linear terms of the corresponding arity. We show that the extension of non-deterministic linear hypersubstitutions of type τ map sets of linear terms to sets of linear terms. As a consequence, the collection of all non-deterministic linear hypersubstitutions forms a monoid. Non-deterministic linear hypersubstitutions can be applied to identities and to algebras of type τ.

How to cite

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Nareupanat Lekkoksung, and Prakit Jampachon. "Non-Deterministic Linear Hypersubstitutions." Discussiones Mathematicae - General Algebra and Applications 35.1 (2015): 97-103. <http://eudml.org/doc/270500>.

@article{NareupanatLekkoksung2015,
abstract = {A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of linear terms of the corresponding arity. We show that the extension of non-deterministic linear hypersubstitutions of type τ map sets of linear terms to sets of linear terms. As a consequence, the collection of all non-deterministic linear hypersubstitutions forms a monoid. Non-deterministic linear hypersubstitutions can be applied to identities and to algebras of type τ.},
author = {Nareupanat Lekkoksung, Prakit Jampachon},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {linear term; non-deterministic linear hypersubstitution},
language = {eng},
number = {1},
pages = {97-103},
title = {Non-Deterministic Linear Hypersubstitutions},
url = {http://eudml.org/doc/270500},
volume = {35},
year = {2015},
}

TY - JOUR
AU - Nareupanat Lekkoksung
AU - Prakit Jampachon
TI - Non-Deterministic Linear Hypersubstitutions
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2015
VL - 35
IS - 1
SP - 97
EP - 103
AB - A non-deterministic hypersubstitution maps operation symbols to sets of terms of the corresponding arity. A non-deterministic hypersubstitution of type τ is said to be linear if it maps any operation symbol to a set of linear terms of the corresponding arity. We show that the extension of non-deterministic linear hypersubstitutions of type τ map sets of linear terms to sets of linear terms. As a consequence, the collection of all non-deterministic linear hypersubstitutions forms a monoid. Non-deterministic linear hypersubstitutions can be applied to identities and to algebras of type τ.
LA - eng
KW - linear term; non-deterministic linear hypersubstitution
UR - http://eudml.org/doc/270500
ER -

References

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  1. [1] T. Changphas, K. Denecke and B. Pibaljommee, Linear terms and linear hypersubstitutions, preprint (2014), Khon Kaen. 
  2. [2] M. Couceiro and E. Lehtonen, Galois theory for sets of operations closed under permutation, cylindrification and composition, Algebra Universalis 67 (2012) 273-297. doi: 10.1007/s00012-012-0184-1 Zbl1257.08002
  3. [3] K. Denecke, P. Glubudom and J. Koppitz, Power Clones and Non-Deterministic Hypersubstitutions, Asian-European J. Math. 1 (2) (2008) 177-188. doi: 10.1142/s1793557108000175 Zbl1221.08002
  4. [4] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach science Publishers (2000). doi: 10.5860/choice.39-2238 Zbl0960.08001
  5. [5] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science (Chapman & Hall/CRC, Boca Raton, 2002). 
  6. [6] J. Koppitz and K. Denecke, M-Solid Varieties of Algebras, advances in Mathematics (Springer Science + Business Media, 2006). Zbl1094.08001

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