# [unknown]

Klaus Denecke; Jörg Koppitz; Nittiya Pabhapote

Discussiones Mathematicae - General Algebra and Applications (2008)

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

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topKlaus 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

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

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