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∗ The research of the author was supported by the Alexander v. Humboldt-Stiftung.
The basic concepts are M -hyperidentities, where M is a monoid
of hypersubstitutions. The set of all M -solid varieties of semigroups forms
a complete sublattice of the lattice of all varieties of semigroups. We fix
some specific varieties V of commutative semigroups and study the set of all
M -solid subvarieties of V , in particular, if V is nilpotent.
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