PRESOLID VARIETIES OF n-SEMIGROUPS

The class of all M -solid varieties of a given type τ forms a complete sublattice of the lattice L(τ) of all varieties of algebras of type τ . 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.