# On the maximal subsemigroups of the semigroup of all monotone transformations

Iliya Gyudzhenov; Ilinka Dimitrova

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 26, Issue: 2, page 199-217
- ISSN: 1509-9415

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topIliya Gyudzhenov, and Ilinka Dimitrova. "On the maximal subsemigroups of the semigroup of all monotone transformations." Discussiones Mathematicae - General Algebra and Applications 26.2 (2006): 199-217. <http://eudml.org/doc/276874>.

@article{IliyaGyudzhenov2006,

abstract = {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 $J̃_\{n-1\}$.},

author = {Iliya Gyudzhenov, Ilinka Dimitrova},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {transformation semigroup; maximal subsemigroups; idempotent; isotone; antitone and monotone transformations; Green's equivalences; monotone transformations; semigroups of transformations},

language = {eng},

number = {2},

pages = {199-217},

title = {On the maximal subsemigroups of the semigroup of all monotone transformations},

url = {http://eudml.org/doc/276874},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Iliya Gyudzhenov

AU - Ilinka Dimitrova

TI - On the maximal subsemigroups of the semigroup of all monotone transformations

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 26

IS - 2

SP - 199

EP - 217

AB - 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 $J̃_{n-1}$.

LA - eng

KW - transformation semigroup; maximal subsemigroups; idempotent; isotone; antitone and monotone transformations; Green's equivalences; monotone transformations; semigroups of transformations

UR - http://eudml.org/doc/276874

ER -

## References

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