# All Regular Elements in HypG(2)

Puninagool, Wattapong;Leeratanavalee, Sorasak

• Accepted : 2010.09.27
• Published : 2011.06.30
• 24 9

#### Abstract

In this paper we consider mappings ${\sigma}$ which map the binary operation symbol f to the term ${\sigma}$(f) which do not necessarily preserve the arities. We call these mappings generalized hypersubstitutions. Any generalized hypersubstitution ${\sigma}$ can be extended to a mapping $\hat{\sigma}$ on the set of all terms of type ${\tau}$ = (2). We de ne a binary operation on the set $Hyp_G$(2) of all generalized hypersubstitutions of type ${\tau}$ = (2) by using this extension The set $Hyp_G$(2) together with the identity generalized hypersubstitution ${\sigma}_{id}$ which maps f to the term f($x_1,x_2$) forms a monoid. We determine all regular elements of this monoid.

#### Keywords

generalized hypersubstitution;regular elements

#### References

1. Denecke, K., Lau, D., Poschel, R., Schweigert, D., Hyperidentities, Hyperequational Classes, and Clone Congruences, Contributions to General Algebra 7, Verlag Holder-Pichler-Tempsky, Wien, (1991), 97-118.
2. Howie, J. M., An Introduction to Semigroup Theory, Academic Press Inc., London, 1976.
3. Koppitz, J. and Denecke, K., M-Solid Varieties of Algebras, Springer Science+Business Media, Inc., New York, 2006.
4. Leeratanavalee, S., Structural Properties of Generalized Hypersubstitutions, Kyungpook Mathematical Journal, 44(2004), 261-267.
5. Leeratanavalee, S. and Denecke, K., Generalized Hypersubstitutions and Strongly Solid Varieties, In General Algebra and Applications, Proc. of the "59 th Workshop on General Algebra", "15 th Conference for Young Algebraists Potsdam 2000", Shaker Verlag(2000), 135-145.

#### Cited by

1. NATURAL PARTIAL ORDERING ON E(HypG(2)) vol.06, pp.02, 2013, https://doi.org/10.1142/S1793557113500162
2. The Relationship between Some Regular Subsemigroups ofHypG2 vol.2014, 2014, https://doi.org/10.1155/2014/181397