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2008 | 28 | 1 | 91-119
Tytuł artykułu

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

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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.
Twórcy
  • University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
  • University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
  • 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.
Typ dokumentu
Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1137
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