Geodesic
Maximal submonoids of monoids of hypersubstitutions
Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 69-85

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For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ = (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], [12]) to describe monoids of transformation hypersubstitutions.
Keywords: regular hypersubstitutions, maximal monoids of hypersubstitutions, transformation semigroups 
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Dimitrova, Ilinka; Koppitz, Jörg. Maximal submonoids of monoids of hypersubstitutions. Discussiones Mathematicae. General Algebra and Applications, Tome 27 (2007) no. 1, pp. 69-85. http://geodesic.mathdoc.fr/item/DMGAA_2007_27_1_a4/