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Maximal submonoids of monoids of hypersubstitutions

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Dimitrova I., Koppitz J.

Discussiones Mathematicae - General Algebra and Applications

2007

tom 27

nr 1

69-85

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.

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1 Discussiones Mathematicae - General Algebra and Applications

1 Dimitrova I.

1 Koppitz J.

1 2006

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Maximal submonoids of monoids of hypersubstitutions