On the maximal subsemigroups of the semigroup of all monotone transformations

• Autorzy: Iliya Gyudzhenov , Ilinka Dimitrova
• Języki publikacji: EN

Abstrakty

EN

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 $J̃_{n-1}$.

Słowa kluczowe

EN

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

Kategorie tematyczne

• 20M20: Semigroups of transformations, etc.

• Wydawca: Faculty of Mathematics, Computer Science and Econometrics, University of Zielona Góra
• Czasopismo: Discussiones Mathematicae - General Algebra and Applications
• Rocznik: 2006
• Tom: 26
• Numer: 2
• Strony: 199-217

Daty

wydano

2006

otrzymano

2006-07-10

poprawiono

2006-09-13

Twórcy

autor

Iliya Gyudzhenov

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

autor

Ilinka Dimitrova

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

Bibliografia

• [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.

Identyfikatory

DOI

10.7151/dmgaa.1112