# 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

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topNareupanat 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

top- [1] T. Changphas, K. Denecke and B. Pibaljommee, Linear terms and linear hypersubstitutions, preprint (2014), Khon Kaen.
- [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] 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] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach science Publishers (2000). doi: 10.5860/choice.39-2238 Zbl0960.08001
- [5] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science (Chapman & Hall/CRC, Boca Raton, 2002).
- [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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