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Discussiones Mathematicae General Algebra and Applications 25(2) (2005) 221-233
DOI: https://doi.org/10.7151/dmgaa.1100

PRESOLID VARIETIES OF n-SEMIGROUPS

Avapa Chantasartrassmee The University of the Thai Chamber of Commerce Department of Mathematics 126/1 Vibhavadee-Rangsit Road Din Daeng Bangkok 10400, Thailand e-mail: avapa_a@hotmail.com

Jörg Koppitz University of Potsdam, Institute of Mathematics Am Neuen Palais, 14415 Potsdam, Germany e-mail: koppitz@rz.uni-potsdam.de

Abstract

The class of all M-solid varieties of a given type t forms a complete sublattice of the lattice L(t) of all varieties of algebrasof type t. This gives a tool for a better description of the latticeL(t) 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 Ł i ≤ j Ł 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 ł 3.

Keywords: hypersubstitution, presolid, n-semigroup.

2000 Mathematics Subject Classification: 08B15, 08B25.

References

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Received 15 July 2005