Geodesic
Presolid varieties of n-semigroups
Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 221-233.

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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.
Keywords: hypersubstitution, presolid, n-semigroup 
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Chantasartrassmee, Avapa; Koppitz, Jörg. Presolid varieties of n-semigroups. Discussiones Mathematicae. General Algebra and Applications, Tome 25 (2005) no. 2, pp. 221-233. http://geodesic.mathdoc.fr/item/DMGAA_2005_25_2_a4/

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