All completely regular elements in H y p G ( n )

Ampika Boonmee; Sorasak Leeratanavalee

Discussiones Mathematicae - General Algebra and Applications (2013)

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

Abstract

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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).

How to cite

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Ampika 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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  1. [1] J. Aczèl, Proof of a theorem of distributive type hyperidentities, Algebra Universalis 1 (1971) 1-6. 
  2. [2] V.D. Belousov, System of quasigroups with generalized identities, Uspechi Mat. Nauk. 20 (1965) 75-146. Zbl0135.03503
  3. [3] A. Boonmee and S. Leeratanavalee, Factorisable of Generalized Hypersubstitutions of type τ=(2), Wulfenia Journal 20 (9) (2013) 245-258. Zbl06537809
  4. [4] K. Denecke, D. Lau, R. Pöschel and D. Schweigert, Hyperidentities, hyperequational classes and clone congruences, Contributions to General Algebra 7, Verlag Hölder-Pichler-Tempsky, Wein (1991) 97-118. Zbl0759.08005
  5. [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
  6. [6] J.M. Howie, Fundamentals of Semigroup Theory (Academic Press, London, 1995). 
  7. [7] M. Petrich and N.R. Reilly, Completely Regular Semigroups (John Wiley and Sons, Inc., New York, 1999). Zbl0967.20034
  8. [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. 
  9. [9] W.D. Newmann, Mal'cev conditions, spectra and Kronecker product, J. Austral. Math. Soc (A) 25 (1987) 103-117. 
  10. [10] W. Taylor, Hyperidentities and hypervarieties, Aequationes Math. 23 (1981) 111-127. Zbl0491.08009

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