# The Order of Normal Form Generalized Hypersubstitutions of Type τ = (2)

Sudsanit, Sivaree;Leeratanavalee, Sorasak

• Accepted : 2013.04.15
• Published : 2014.09.23
• 16 6

#### Abstract

In 2000, K. Denecke and K. Mahdavi showed that there are many idempotent elements in $Hyp_{N_{\varphi}}(V)$ the set of normal form hypersubstitutions of type ${\tau}=(2)$ which are not idempotent elements in Hyp(2) the set of all hypersubstitutions of type ${\tau}=(2)$. They considered in which varieties, idempotent elements of Hyp(2) are idempotent elements of $Hyp_{N_{\varphi}}(V)$. In this paper, we study the similar problems on the set of all generalized hypersubstitutions of type ${\tau}=(2)$ and the set of all normal form generalize hypersubstitutions of type ${\tau}=(2)$ and determine the order of normal form generalize hypersubstitutions of type ${\tau}=(2)$.

#### Keywords

Order;normal form generalized hypersubstitution;idempotent element

#### References

1. K. Denecke, K. Mahdavi, The Order of Normal Form Hypersubstitutions of Type (2), Discussiones Mathematicae General Algebra and Applications, 20(2000), 183-192. https://doi.org/10.7151/dmgaa.1015
2. K. Denecke, Sh. L. Wismath, Hyperidentities and clones, Gordon and Breach Sci. Publ., Amsterdam-Singapore(2000).
3. S. Leeratanavalee, K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, In General and Applications, Proc. of "59th Workshop on General Algebra ", "15th Conference for Young Algebraists Potsdam 2000", Shaker Verlag(2000), 135-145.
4. S. Leeratanavalee, S. Phatchat, Pre-Strongly Solid and Left-Edge (Right-Edge)-Strongly Solid Varieties of Semigroups, International Journal of Algebra, 1(5)(2007), 205-226. https://doi.org/10.12988/ija.2007.07021
5. J. P lonka, Proper and Inner Hypersubstitutions of Varieties, In proceedings of the International Conference : Summer School on General Algebra and Ordered Set 1994, Palacky University Olomouc (1994), 106-115.
6. W. Puninagool, S. Leeratanavalee, The Order of Generalized Hypersubstitutions of Type ${\tau}$ = (2), International Journal of Mathematics and Mathematical Science, Vol. 2008, Article ID 263541, 8 pages,doi:10.1155/2008/263541. https://doi.org/10.1155/2008/263541