Geodesic
Non-Deterministic Linear Hypersubstitutions
Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 97-103.

Voir la notice de l'article provenant de la source Library of Science

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.
Keywords: linear term, non-deterministic linear hypersubstitution 
@article{DMGAA_2015_35_1_a7,
     author = {Lekkoksung, Nareupanat and Jampachon, Prakit},
     title = {Non-Deterministic {Linear} {Hypersubstitutions}},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {97--103},
     publisher = {mathdoc},
     volume = {35},
     number = {1},
     year = {2015},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a7/}
}
TY  - JOUR
AU  - Lekkoksung, Nareupanat
AU  - Jampachon, Prakit
TI  - Non-Deterministic Linear Hypersubstitutions
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2015
SP  - 97
EP  - 103
VL  - 35
IS  - 1
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a7/
LA  - en
ID  - DMGAA_2015_35_1_a7
ER  - 
%0 Journal Article
%A Lekkoksung, Nareupanat
%A Jampachon, Prakit
%T Non-Deterministic Linear Hypersubstitutions
%J Discussiones Mathematicae. General Algebra and Applications
%D 2015
%P 97-103
%V 35
%N 1
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a7/
%G en
%F DMGAA_2015_35_1_a7
Lekkoksung, Nareupanat; Jampachon, Prakit. Non-Deterministic Linear Hypersubstitutions. Discussiones Mathematicae. General Algebra and Applications, Tome 35 (2015) no. 1, pp. 97-103. http://geodesic.mathdoc.fr/item/DMGAA_2015_35_1_a7/

[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

[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

[4] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach science Publishers (2000). doi: 10.5860/choice.39-2238

[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).