# Binary relations on the monoid of V-proper hypersubstitutions

Klaus Denecke; Rattana Srithus

Discussiones Mathematicae - General Algebra and Applications (2006)

- Volume: 26, Issue: 2, page 233-251
- ISSN: 1509-9415

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topKlaus Denecke, and Rattana Srithus. "Binary relations on the monoid of V-proper hypersubstitutions." Discussiones Mathematicae - General Algebra and Applications 26.2 (2006): 233-251. <http://eudml.org/doc/276895>.

@article{KlausDenecke2006,

abstract = {In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.},

author = {Klaus Denecke, Rattana Srithus},

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

keywords = {solid variety; degree of proper hypersubstitutions; isomorphism degree of proper hypersubstitutions; proper hypersubstitution; monoid of hypersubstitutions},

language = {eng},

number = {2},

pages = {233-251},

title = {Binary relations on the monoid of V-proper hypersubstitutions},

url = {http://eudml.org/doc/276895},

volume = {26},

year = {2006},

}

TY - JOUR

AU - Klaus Denecke

AU - Rattana Srithus

TI - Binary relations on the monoid of V-proper hypersubstitutions

JO - Discussiones Mathematicae - General Algebra and Applications

PY - 2006

VL - 26

IS - 2

SP - 233

EP - 251

AB - In this paper we consider different relations on the set P(V) of all proper hypersubstitutions with respect to a given variety V and their properties. Using these relations we introduce the cardinalities of the corresponding quotient sets as degrees and determine the properties of solid varieties having given degrees. Finally, for all varieties of bands we determine their degrees.

LA - eng

KW - solid variety; degree of proper hypersubstitutions; isomorphism degree of proper hypersubstitutions; proper hypersubstitution; monoid of hypersubstitutions

UR - http://eudml.org/doc/276895

ER -

## References

top- [1] St. Burris and H.P. Sankappanavar, A course in Universal Algebra, Springer-Verlag, New York, Heidelberg, Berlin 1981.
- [2] K. Denecke and J. Koppitz, Fluid, unsolid, and completely unsolid varieties, Algebra Colloquium 7:4 (2000), 381-390. Zbl0969.08004
- [3] K. Denecke and R. Marszałek, Binary Relations on Monoids of Hypersubstitutions, Algebra Colloquium 4:1 (1997), 49-64. Zbl0877.20040
- [4] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Science Publishers, 2000.
- [5] K. Denecke and S.L. Wismath, Universal Algebra and Applications in Theoretical Computer Science, Boca Raton, London, Washington, D.C.: Chapman & Hall/CRC 2002.
- [6] K. Denecke, J. Koppitz and R. Srithus, The Degree of Proper Hypersubstitutions, preprint 2005. Zbl1139.08003
- [7] K. Denecke, J. Koppitz and R. Srithus, N-fluid Varieties, preprint 2005.
- [8] E. Graczyńska, M-solid Quasivarieties, preprint 2006.
- [9] E. Graczyńska and D. Schweigert, The Dimension of a Variety, preprint 2006. Zbl1137.08004
- [10] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2006. Zbl1094.08001
- [11] J. Płonka, Proper and inner hypersubstitutions of varieties, p. 106-116 in: 'Proceedings of the International Conference Sommer School on General Algebra and Ordered Sets', Olomouc 1994. Zbl0828.08003

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