# Maximal submonoids of monoids of hypersubstitutions

Ilinka Dimitrova; Jörg Koppitz

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 27, Issue: 1, page 69-85
- ISSN: 1509-9415

## Access Full Article

top## Abstract

top## How to cite

topIlinka Dimitrova, and Jörg Koppitz. "Maximal submonoids of monoids of hypersubstitutions." Discussiones Mathematicae - General Algebra and Applications 27.1 (2006): 69-85. <http://eudml.org/doc/276921>.

@article{IlinkaDimitrova2006,

abstract = {For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ = (n) (introduced in [4]). The concept of a transformation hypersubstitution, introduced in [1], gives a relationship between monoids of hypersubstitutions and transformation semigroups. In the present paper, we apply the recent results about transformation semigroups by I. Guydzenov and I. Dimitrova ([11], [12]) to describe monoids of transformation hypersubstitutions.},

author = {Ilinka Dimitrova, Jörg Koppitz},

journal = {Discussiones Mathematicae - General Algebra and Applications},

keywords = {regular hypersubstitutions; maximal monoids of hypersubstitutions; transformation semigroups; hypersubstitution; maximal submonoid; transformation semigroup},

language = {eng},

number = {1},

pages = {69-85},

title = {Maximal submonoids of monoids of hypersubstitutions},

url = {http://eudml.org/doc/276921},

volume = {27},

year = {2006},

}

TY - JOUR

AU - Ilinka Dimitrova

AU - Jörg Koppitz

TI - Maximal submonoids of monoids of hypersubstitutions

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 27

IS - 1

SP - 69

EP - 85

AB - For a monoid M of hypersubstitutions, the collection of all M-solid varieties forms a complete sublattice of the lattice L(τ) of all varieties of a given type τ. Therefore, by the study of monoids of hypersubstitutions one can get more insight into the structure of the lattice L(τ). In particular, monoids of hypersubstitutions were studied in [9] as well as in [5]. We will give a complete characterization of all maximal submonoids of the monoid Reg(n) of all regular hypersubstitutions of type τ = (n) (introduced in [4]). The concept of a transformation hypersubstitution, introduced in [1], gives a relationship between monoids of hypersubstitutions and transformation semigroups. In the present paper, we apply the recent results about transformation semigroups by I. Guydzenov and I. Dimitrova ([11], [12]) to describe monoids of transformation hypersubstitutions.

LA - eng

KW - regular hypersubstitutions; maximal monoids of hypersubstitutions; transformation semigroups; hypersubstitution; maximal submonoid; transformation semigroup

UR - http://eudml.org/doc/276921

ER -

## References

top- [1] V. Budd, K. Denecke and S.L. Wismath, Short Solid Superassociative Type (n) Varieties, East-West Journal of Mathematics 2 (2) (2001), 129-145. Zbl1008.08004
- [2] Th. Changphas, Monoids of Hypersubstitutions, Dissertation, Universität Potsdam 2004. Zbl1108.08300
- [3] Th. Changphas and K. Denecke, Full Hypersubstitutions and Full Solid Varieties of Semigroups, East-West Journal of Mathematics 4 (1) (2002), 177-193.
- [4] K. Denecke and J. Koppitz, M-Solid Varieties of Semigroups, Discuss. Math. 15 (1995), 23-41. Zbl0842.20050
- [5] K. Denecke and J. Koppitz, M-Solid Varieties of Algebras, Springer Science-Business Media 2006. Zbl1094.08001
- [6] K. Denecke, J. Koppitz and S. Niwczyk, Equational theories generated by hypersubstitutions of type] (n), Int. Journal of Algebra and Computation 12 (6) (2002), 867-876. Zbl1051.08003
- [7] K. Denecke, J. Koppitz and S. Shtrakov, The Depth of a Hypersubstitution, Journal of Automata, Languages and Combinatorics 6 (3) (2001), 253-262. Zbl0993.68052
- [8] K. Denecke and M. Reichel, Monoids of hypersubstitutions and M-solid varieties, Contributions to General Algebra 9, Wien 1995, 117-126. Zbl0884.08008
- [9] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Scientific Publishers, 2000.
- [10] K. Denecke and S.L. Wismath, Complexity of Terms, Composition, and Hypersubstitution, Int. Journal of Mathematics and Mathematical Sciences 15 (2003), 959-969. Zbl1015.08005
- [11] 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. Zbl1072.20079
- [12] Il. Gyudzhenov and Il. Dimitrova, On the Maximal Subsemigroups of the Semigroup of All Isotone Transformations with Defect ≥ 2, Comptes rendus de l'Academie bulgare des Sciences 59 (3) (2006), 239-244. Zbl1104.20059
- [13] Il. Gyudzhenov and Il. Dimitrova, On the Maximal Subsemigroups of the Semigroup of all Monotone Transformations, Discuss. Math., submitted.
- [14] J.M. Howie, An Introduction to Semigroup Theory, Academic Press, London 1976. Zbl0355.20056
- [15] M.W. Liebeck, C.E. Praeger and J. Saxl, A Classification of the Maximal Subgroups of the Finite Alternating and Symmetric Groups, Journal of Algebra 111 (1987), 365-383. Zbl0632.20011
- [16] X. Yang, A Classification of Maximal Subsemigroups of Finite Order-Preserving Transformation Semigroups, Communications in Algebra 28 (3) (2000), 1503-1513. Zbl0948.20039

## NotesEmbed ?

topTo embed these notes on your page include the following JavaScript code on your page where you want the notes to appear.