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

Abstract

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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 J ̃ 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 J ̃ n - 1 .

How to cite

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Iliya 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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  1. [1] H. Clifford and G.B. Preston, The algebraic theory of semigroups, 1. Amer. Math. Soc., Providence, 1961, MR 24#A2627. 
  2. [2] V.H. Fernandes, G.M.S. Gomes and M.M. Jesus, Presentations for Some Monoids of Partial Transformations on a Finite Chain, Communications in Algebra 33 (2005), 587-604. Zbl1072.20079
  3. [3] Il. Gyudzhenov and Il. Dimitrova, On Properties of Idempotents of the Semigroup of Isotone Transformations and it Structure, Comptes rendus de l'Academie bulgare des Sciences, to appear. 
  4. [4] J.M. Howie, Products of Idempotents in Certain Semigroups of Transformations, Proc. Edinburgh Math. Soc. 17 (2) (1971), 223-236. Zbl0226.20072
  5. [5] J.W. Nichols, A Class of Maximal Inverse Subsemigroups of T X , Semigroup Forum 13 (1976), 187-188. Zbl0359.20048
  6. [6] N.R. Reilly, Maximal Inverse Subsemigroups of T X , Semigroup Forum, Subsemigroups of Finite Singular Semigroups, Semigroup Forum 15 (1978), 319-326. Zbl0379.20056
  7. [7] Y. Taijie and Y. Xiuliang, A Classification of Maximal Idempotent-Generated, 4 (2002), 243-264. 
  8. [8] K. Todorov and L. Kračolova, On the Rectangular Bands of Groups of D-Classes of the Symmetric Semigroup, Periodica Mathem. Hungarica 13 (2) (1983), 97-104. Zbl0477.20049
  9. [9] Y. Xiuliang, A Classification of Maximal Inverse Subsemigroups of Finite Symmetric Inverse Semigroups, Communications in Algebra 27 (1999), 4089-4096. Zbl0943.20064
  10. [10] Y. Xiuliang, A Classification of Maximal Subsemigroups of Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (3) (2000), 1503-1513. Zbl0948.20039
  11. [11] Y. Xiuliang and Lu Chunghan, Maximal Properties of Some Subsemigroups in Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (2000), 3125-3135. Zbl0952.20049

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