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2005 | 25 | 2 | 221-233
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Presolid varieties of n-semigroups

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EN
he class of all M-solid varieties of a given type t forms a complete sublattice of the lattice ℒ(τ) of all varieties of algebrasof type t. This gives a tool for a better description of the lattice ℒ(τ) by characterization of complete sublattices. In particular, this was done for varieties of semigroups by L. Polák ([10]) as well as by Denecke and Koppitz ([4], [5]). Denecke and Hounnon characterized M-solid varieties of semirings ([3]) and M-solid varieties of groups were characterized by Koppitz ([9]). In the present paper we will do it for varieties of n-semigroups. An n-semigroup is an algebra of type (n), where the operation satisfies the [i,j]-associative laws for 1 ≤ i ≤ j ≤ n, introduced by Dörtnte ([2]). It is clear that the notion of a 2-semigroup is the same as the notion of a semigroup. Here we will consider the case n ≥ 3.
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  • The University of the Thai Chamber of Commerce, Department of Mathematics, 126/1 Vibhavadee-Rangsit Road, Din Daeng Bangkok 10400, Thailand
  • University of Potsdam, Institute of Mathematics, Am Neuen Palais, 14415 Potsdam, Germany
Bibliografia
  • [1] V. Budd, K. Denecke and S.L. Wismath, Short-solid superassociative type (n) varieties, East-West J. of Mathematics 3 (2) (2001), 129-145.
  • [2] W. Dörnte, Untersuchungen über einen verallgemeinerten Gruppenbegriff, Math. Z. 29 (1928), 1-19.
  • [3] K. Denecke and Hounnon, All solid varieties of semirings, Journal of Algebra 248 (2002), 107-117.
  • [4] K. Denecke and J. Koppitz, Pre-solid varieties of semigroups, Archivum Mathematicum 31 (1995), 171-181.
  • [5] K. Denecke and J. Koppitz, Finite monoids of hypersubstitutions of type t = (2), Semigroup Forum 56 (1998), 265-275.
  • [6] K. Denecke and M. Reichel, Monoids of hypersubstitutions and M-solid varieties, Contributions to General Algebra 9 (1995), 117-126.
  • [7] K. Denecke, J. Koppitz and S.L. Wismath, Solid varieties of arbitrary type, Algebra Universalis 48 (2002), 357-378.
  • [8] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Scientific Publisher, 2000.
  • [9] J. Koppitz, Hypersubstitutions and groups, Novi Sad J. Math. 34 (2) (2004), 127-139.
  • [10] L. Polák, All solid varieties of semigroups, Journal of Algebra 219 (1999), 421-436.
  • [11] J. Płonka, Proper and inner hypersubstitutions of varieties, 'Proceedings of the International Conference: 'Summer School on General Algebra and Ordered Sets', Olomouc 1994', Palacký University, Olomouc 1994, 106-115.
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Bibliografia
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bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1100
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