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## Discussiones Mathematicae - General Algebra and Applications

2009 | 29 | 2 | 153-167
Tytuł artykułu

### The maximal subsemigroups of the ideals of some semigroups of partial injections

Autorzy
Treść / Zawartość
Warianty tytułu
Języki publikacji
EN
Abstrakty
EN
We study the structure of the ideals of the semigroup $IO_n$ of all isotone (order-preserving) partial injections as well as of the semigroup $IM_n$ of all monotone (order-preserving or order-reversing) partial injections on an n-element set. The main result is the characterization of the maximal subsemigroups of the ideals of $IO_n$ and $IM_n$.
Słowa kluczowe
EN
Kategorie tematyczne
Rocznik
Tom
Numer
Strony
153-167
Opis fizyczny
Daty
wydano
2009
otrzymano
2009-04-20
poprawiono
2009-11-10
Twórcy
autor
• Faculty of Mathematics and Natural Science, South-West University "Neofit Rilski", Blagoevgrad, 2700, Bulgaria
autor
• Institute of Mathematics, Potsdam University Potsdam, 14469, Germany
Bibliografia
• [1] A.Ja. Aĭzenštat, Defining Relations of the Semigroup of Endomorphisms of a Finite Linearly Ordered Set, Sibirsk. Matem. Žurn. 3 (1962), 161-169.
• [2] M. Delgado and V.H. Fernandes, Abelian Kernels of Some Monoids of Injective Partial Transformations and an Application, Semigroup Forum 61 (2000), 435-452.
• [3] M. Delgado and V.H. Fernandes, Abelian Kernels of Monoids of Order-Preserving Maps and of Some of Its Extensions, Semigroup Forum 68 (2004), 335-356.
• [4] I. Dimitrova and J. Koppitz, On the Maximal Subsemigroups of Some Transformation Semigroups, Asian-European Journal of Mathematics 1 (2) (2008), 189-202.
• [5] I. Dimitrova and J. Koppitz, The Maximal Subsemigroups of the Semigroup of all Monotone Partial Injections, Communications in Algebra, submited.
• [6] V.H. Fernandes, Semigroups of Order-preserving Mappings on a Finite Chain: a new class of divisors, Semigroup Forum 54 (2)(1997), 230-236.
• [7] V.H. Fernandes, The Monoid of All Injective Order-preserving Partial Transformations on a Finite Chain, Semigroup Forum 62 (2001), 178-204.
• [8] V.H. Fernandes, Semigroups of Order-preserving Mappings on a Finite Chain: another class of divisors, Izvestiya VUZ Matematika 3 (478) (2002), 51-59.
• [9] V.H. Fernandes, Presentations for Some Monoids of Partial Transformations on a Finite Chain: a survey, Semigroups, Algorithms, Automata and Languages, World Scientific (2002), 363-378.
• [10] 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.
• [11] V.H. Fernandes G.M.S. Gomes and M.M. Jesus, Presentations for Some Monoids of Injective Partial Transformations on a Finite Chain, Southeast Asian Bull. Math. 28 (2004), 903-918.
• [12] O. Ganyushkin and V. Mazorchuk, On the Structure of $IO_n$, Semigroup Forum 66 (2003), 455-483.
• [13] G.M.S. Gomes and J.M. Howie, On the Rank of Certain Semigroups of Order-preserving Transformations, Semigroup Forum 51 (1992), 275-282.
• [14] J.M. Howie, Products of Idempotents in Certain Semigroups of Transformations, Proc. Edinburgh Math. Soc. 17 (2) (1971), 223-236.
• [15] J.M. Howie and B.M. Shein, Products of Idempotent Order-Preserving Transformations, J. London Math. Soc. 7 (2) (1973), 357-366.
• [16] L.M. Popova, Defining Relations of the Semigroup of Partial Endomorphisms of a Finite Linearly Ordered Set, Leningrad Gos. Ped. Inst. Učen. Zap. 238 (1962), 78-88.
• [17] X. Yang, A Classiffication of Maximal Subsemigroups of Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (3) (2000), 1503-1513.
• [18] X. Yang and Ch. Lu, Maximal Properties of Some Subsemigroups in Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (2000), 3125-3135.
Typ dokumentu
Bibliografia
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