On the maximal subsemigroups of the semigroup of all monotone transformations

Iliya Gyudzhenov; Ilinka Dimitrova

ArticleOriginal scientific text

Title

On the maximal subsemigroups of the semigroup of all monotone transformations

Authors ¹, ¹

Affiliations

South-West University "Neofit Rilski", Faculty of Mathematics and Natural Science, 2700 Blagoevgrad, Bulgaria

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

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}

.

Keywords

ENG

transformation semigroup, maximal subsemigroups, idempotent, isotone, antitone and monotone transformations, Green's equivalences

H. Clifford and G.B. Preston, The algebraic theory of semigroups, 1. Amer. Math. Soc., Providence, 1961, MR 24#A2627.
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.
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.
J.M. Howie, Products of Idempotents in Certain Semigroups of Transformations, Proc. Edinburgh Math. Soc. 17 (2) (1971), 223-236.
J.W. Nichols, A Class of Maximal Inverse Subsemigroups of $T_{X}$ , Semigroup Forum 13 (1976), 187-188.
N.R. Reilly, Maximal Inverse Subsemigroups of $T_{X}$ , Semigroup Forum, Subsemigroups of Finite Singular Semigroups, Semigroup Forum 15 (1978), 319-326.
Y. Taijie and Y. Xiuliang, A Classification of Maximal Idempotent-Generated, 4 (2002), 243-264.
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.
Y. Xiuliang, A Classification of Maximal Inverse Subsemigroups of Finite Symmetric Inverse Semigroups, Communications in Algebra 27 (1999), 4089-4096.
Y. Xiuliang, A Classification of Maximal Subsemigroups of Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (3) (2000), 1503-1513.
Y. Xiuliang and Lu Chunghan, Maximal Properties of Some Subsemigroups in Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (2000), 3125-3135.

Title

On the maximal subsemigroups of the semigroup of all monotone transformations

Affiliations

Abstract

Keywords

Bibliography