Geodesic
On the maximal subsemigroups of the semigroup of all monotone transformations
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 199-217 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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.
Keywords: transformation semigroup, maximal subsemigroups, idempotent, isotone, antitone and monotone transformations, Green's equivalences 
@article{DMGAA_2006_26_2_a4,
     author = {Gyudzhenov, Iliya and Dimitrova, Ilinka},
     title = {On the maximal subsemigroups of the semigroup of all monotone transformations},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     pages = {199--217},
     year = {2006},
     volume = {26},
     number = {2},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a4/}
}
TY  - JOUR
AU  - Gyudzhenov, Iliya
AU  - Dimitrova, Ilinka
TI  - On the maximal subsemigroups of the semigroup of all monotone transformations
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2006
SP  - 199
EP  - 217
VL  - 26
IS  - 2
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a4/
LA  - en
ID  - DMGAA_2006_26_2_a4
ER  - 
%0 Journal Article
%A Gyudzhenov, Iliya
%A Dimitrova, Ilinka
%T On the maximal subsemigroups of the semigroup of all monotone transformations
%J Discussiones Mathematicae. General Algebra and Applications
%D 2006
%P 199-217
%V 26
%N 2
%U http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a4/
%G en
%F DMGAA_2006_26_2_a4
Gyudzhenov, Iliya; Dimitrova, Ilinka. On the maximal subsemigroups of the semigroup of all monotone transformations. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 199-217. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a4/

[1] H. Clifford and G.B. Preston, The algebraic theory of semigroups, 1. Amer. Math. Soc., Providence, 1961, MR 24#A2627.

[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.

[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] J.M. Howie, Products of Idempotents in Certain Semigroups of Transformations, Proc. Edinburgh Math. Soc. 17 (2) (1971), 223-236.

[5] J.W. Nichols, A Class of Maximal Inverse Subsemigroups of $T_X$, Semigroup Forum 13 (1976), 187-188.

[6] N.R. Reilly, Maximal Inverse Subsemigroups of $T_X$, Semigroup Forum, Subsemigroups of Finite Singular Semigroups, Semigroup Forum 15 (1978), 319-326.

[7] Y. Taijie and Y. Xiuliang, A Classification of Maximal Idempotent-Generated, 4 (2002), 243-264.

[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.

[9] Y. Xiuliang, A Classification of Maximal Inverse Subsemigroups of Finite Symmetric Inverse Semigroups, Communications in Algebra 27 (1999), 4089-4096.

[10] Y. Xiuliang, A Classification of Maximal Subsemigroups of Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (3) (2000), 1503-1513.

[11] Y. Xiuliang and Lu Chunghan, Maximal Properties of Some Subsemigroups in Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (2000), 3125-3135.