Maximal submonoids of monoids of hypersubstitutions
Ilinka Dimitrova, Jörg Koppitz · Discussiones Mathematicae - General Algebra and Applications · 2007
For a monoid M of hypersubstitutions, the collection of all M -solid varieties forms a complete sublattice of the lattice L( ) of all varieties of a given type . Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L( ). In particular, monoids of hypersubstitutions were studied in We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type = (n) (introduced in [4]). The concept of a transformation hypersubstitution, introduced in [1], gives a relationship between monoids of hypersubstitutions and transformation semigroups. In the present paper, we apply the recent results about transformation semigroups by I. Guydzenov and I. Dimitrova ([11],