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Klaus Denecke; Jörg Koppitz; Nittiya Pabhapote

Discussiones Mathematicae - General Algebra and Applications (2008)

  • Volume: 28, Issue: 1, page 91-119
  • ISSN: 1509-9415

Abstract

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A regular hypersubstitution is a mapping which takes every n i -ary operation symbol to an n i -ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities.

How to cite

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Klaus Denecke, Jörg Koppitz, and Nittiya Pabhapote. "null." Discussiones Mathematicae - General Algebra and Applications 28.1 (2008): 91-119. <http://eudml.org/doc/276942>.

@article{KlausDenecke2008,
abstract = {A regular hypersubstitution is a mapping which takes every $n_i$-ary operation symbol to an $n_i$-ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities.},
author = {Klaus Denecke, Jörg Koppitz, Nittiya Pabhapote},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {hypersubstitutions; terms; regular-solid variety; solid variety; finite axiomatizability; regular-solid varieties of semigroups; finitely based varieties},
language = {eng},
number = {1},
pages = {91-119},
url = {http://eudml.org/doc/276942},
volume = {28},
year = {2008},
}

TY - JOUR
AU - Klaus Denecke
AU - Jörg Koppitz
AU - Nittiya Pabhapote
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2008
VL - 28
IS - 1
SP - 91
EP - 119
AB - A regular hypersubstitution is a mapping which takes every $n_i$-ary operation symbol to an $n_i$-ary term. A variety is called regular-solid if it contains all algebras derived by regular hypersubstitutions. We determine the greatest regular-solid variety of semigroups. This result will be used to give a new proof for the equational description of the greatest solid variety of semigroups. We show that every variety of semigroups which is finitely based by hyperidentities is also finitely based by identities.
LA - eng
KW - hypersubstitutions; terms; regular-solid variety; solid variety; finite axiomatizability; regular-solid varieties of semigroups; finitely based varieties
UR - http://eudml.org/doc/276942
ER -

References

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  1. [1] Sr. Arworn, Groupoids of Hypersubstitutions and G-solid Varieties, Shaker-Verlag, Aachen 2000. 
  2. [2] K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Science Publishers 2000. Zbl0960.08001
  3. [3] O.C. Kharlampovitsch and M.V. Sapir, Algorithmic problems in varieties, Int. J. Algebra and Computation 5 (1995), 379-602. Zbl0837.08002
  4. [4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2006. Zbl1094.08001
  5. [5] P. Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1968), 298-314. Zbl0186.03401
  6. [6] J. Płonka, Proper and inner hypersubstitutions of varieties, pp. 421-436 in: 'Proceedings of the International Conference Summer School on General Algebra and Ordered Sets', Olomouc 1994. Zbl0828.08003
  7. [7] L. Polák, On Hyperassociativity, Algebra Universalis 36 (3) (1996), 363-378. 
  8. [8] L. Polák, All solid varieties of semigroups, J. of Algebra 2 (1999), 421-436. Zbl0935.20050
  9. [9] D. Schweigert, Hyperidentities, pp. 405-506 in: Algebras and Orders, Kluwer 1993. 

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