Binary relations on the monoid of V-proper hypersubstitutions
Klaus Denecke ; Rattana Srithus
Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006), p. 233-251 / Harvested from The Polish Digital Mathematics Library

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.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:276895
@article{bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1114,
     author = {Klaus Denecke and Rattana Srithus},
     title = {Binary relations on the monoid of V-proper hypersubstitutions},
     journal = {Discussiones Mathematicae - General Algebra and Applications},
     volume = {26},
     year = {2006},
     pages = {233-251},
     zbl = {1141.08005},
     language = {en},
     url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1114}
}
Klaus Denecke; Rattana Srithus. Binary relations on the monoid of V-proper hypersubstitutions. Discussiones Mathematicae - General Algebra and Applications, Tome 26 (2006) pp. 233-251. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_7151_dmgaa_1114/

[000] [1] St. Burris and H.P. Sankappanavar, A course in Universal Algebra, Springer-Verlag, New York, Heidelberg, Berlin 1981.

[001] [2] K. Denecke and J. Koppitz, Fluid, unsolid, and completely unsolid varieties, Algebra Colloquium 7:4 (2000), 381-390. | Zbl 0969.08004

[002] [3] K. Denecke and R. Marszałek, Binary Relations on Monoids of Hypersubstitutions, Algebra Colloquium 4:1 (1997), 49-64. | Zbl 0877.20040

[003] [4] K. Denecke and S.L. Wismath, Hyperidentities and clones, Gordon and Breach Science Publishers, 2000.

[004] [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.

[005] [6] K. Denecke, J. Koppitz and R. Srithus, The Degree of Proper Hypersubstitutions, preprint 2005. | Zbl 1139.08003

[006] [7] K. Denecke, J. Koppitz and R. Srithus, N-fluid Varieties, preprint 2005.

[007] [8] E. Graczyńska, M-solid Quasivarieties, preprint 2006.

[008] [9] E. Graczyńska and D. Schweigert, The Dimension of a Variety, preprint 2006. | Zbl 1137.08004

[009] [10] J. Koppitz and K. Denecke, M-solid Varieties of Algebras, Springer 2006. | Zbl 1094.08001

[010] [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. | Zbl 0828.08003