# All completely regular elements in $Hy{p}_{G}\left(n\right)$

Ampika Boonmee; Sorasak Leeratanavalee

Discussiones Mathematicae - General Algebra and Applications (2013)

- Volume: 33, Issue: 2, page 211-219
- ISSN: 1509-9415

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topAmpika Boonmee, and Sorasak Leeratanavalee. "All completely regular elements in $Hyp_{G}(n)$." Discussiones Mathematicae - General Algebra and Applications 33.2 (2013): 211-219. <http://eudml.org/doc/270659>.

@article{AmpikaBoonmee2013,

abstract = {
In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties.
Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In this paper, we determine the set of all completely regular elements of this monoid of type τ=(n).
},

author = {Ampika Boonmee, Sorasak Leeratanavalee},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {generalized hypersubstitution; regular element; completely regular element; generalized hypersubstitutions; hypervarieties; strong identities; completely regular elements},

language = {eng},

number = {2},

pages = {211-219},

title = {All completely regular elements in $Hyp_\{G\}(n)$},

url = {http://eudml.org/doc/270659},

volume = {33},

year = {2013},

}

TY - JOUR

AU - Ampika Boonmee

AU - Sorasak Leeratanavalee

TI - All completely regular elements in $Hyp_{G}(n)$

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2013

VL - 33

IS - 2

SP - 211

EP - 219

AB -
In Universal Algebra, identities are used to classify algebras into collections, called varieties and hyperidentities are use to classify varieties into collections, called hypervarities. The concept of a hypersubstitution is a tool to study hyperidentities and hypervarieties.
Generalized hypersubstitutions and strong identities generalize the concepts of a hypersubstitution and of a hyperidentity, respectively. The set of all generalized hypersubstitutions forms a monoid. In this paper, we determine the set of all completely regular elements of this monoid of type τ=(n).

LA - eng

KW - generalized hypersubstitution; regular element; completely regular element; generalized hypersubstitutions; hypervarieties; strong identities; completely regular elements

UR - http://eudml.org/doc/270659

ER -

## References

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- [5] W. Puninagool and S. Leeratanavalee, The Monoid of Generalized Hypersubstitutions of type τ=(n), Discuss. Math. General Algebra and Applications 30 (2010) 173-191. doi: 10.7151/dmgaa.1168. Zbl1245.08003
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- [8] S. Leeratanavalee and K. Denecke, Generalized Hypersubstitutions and Strongly Solid Varieties, 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.
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