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.

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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 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 
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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.