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On the maximal subsemigroups of the semigroup of all monotone transformations

100%
Gyudzhenov I., Dimitrova I.
Discussiones Mathematicae - General Algebra and Applications
|
2006
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tom 26
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nr 2
199-217
EN
In this paper we consider the semigroup Mₙ of all monotone transformations on the chain Xₙ under the operation of composition of transformations. First we give a presentation of the semigroup Mₙ and some propositions connected with its structure. Also, we give a description and some properties of the class $J̃_{n-1}$ of all monotone transformations with rank n-1. After that we characterize the maximal subsemigroups of the semigroup Mₙ and the subsemigroups of Mₙ which are maximal in $J̃_{n-1}$.
2
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Maximal submonoids of monoids of hypersubstitutions

100%
Dimitrova I., Koppitz J.
Discussiones Mathematicae - General Algebra and Applications
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2007
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tom 27
|
nr 1
69-85
EN
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.
3
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The maximal subsemigroups of the ideals of some semigroups of partial injections

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Dimitrova I., Koppitz J.
Discussiones Mathematicae - General Algebra and Applications
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2009
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tom 29
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nr 2
153-167
EN
We study the structure of the ideals of the semigroup $IO_n$ of all isotone (order-preserving) partial injections as well as of the semigroup $IM_n$ of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of $IO_n$ and $IM_n$.
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