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/