Geodesic
Binary relations on the monoid of V-proper hypersubstitutions
Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 233-251

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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.
Keywords: solid variety, degree of proper hypersubstitutions, isomorphism degree of proper hypersubstitutions 
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Denecke, Klaus; Srithus, Rattana. Binary relations on the monoid of V-proper hypersubstitutions. Discussiones Mathematicae. General Algebra and Applications, Tome 26 (2006) no. 2, pp. 233-251. http://geodesic.mathdoc.fr/item/DMGAA_2006_26_2_a6/