The greatest regular-solid variety of semigroups % Dedicated to R. McKenzie's 60$^th$ birthday %

• Autorzy: Klaus Denecke , Jörg Koppitz , Nittiya Pabhapote
• Języki publikacji: EN

Abstrakty

EN

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.

Słowa kluczowe

EN

hypersubstitutions; terms; regular-solid variety; solid variety; finite axiomatizability

Kategorie tematyczne

• 20M14: Commutative semigroups
• 20M07: Varieties and pseudovarieties of semigroups

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2008
• Tom: 28
• Numer: 1
• Strony: 91-119

Daty

wydano

2008

otrzymano

2007-04-25

poprawiono

2007-06-16

Twórcy

autor

Klaus Denecke

• University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Jörg Koppitz

• University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany

autor

Nittiya Pabhapote

• The University of the Thai Chamber of Commerce, Department of Mathematics, 126/1 Vibhavadee Rangsit Road, Bangkok, 10400 Thailand

Bibliografia

• [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.
• [3] O.C. Kharlampovitsch and M.V. Sapir, Algorithmic problems in varieties, Int. J. Algebra and Computation 5 (1995), 379-602.
• [4] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2006.
• [5] P. Perkins, Bases for equational theories of semigroups, J. Algebra 11 (1968), 298-314.
• [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.
• [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.
• [9] D. Schweigert, Hyperidentities, pp. 405-506 in: Algebras and Orders, Kluwer 1993.

Identyfikatory

DOI

10.7151/dmgaa.1137