Mathematicae General Algebra and Applications 21(2) (2001)175-200
Klaus Denecke, Jörg Koppitz
University of Potsdam, Institute of Mathematics,
Department of Mathematics and C.S., University of
We prove that the semantical kernel of a hypersubstitution is a fully invariant congruence relation on the absolutely free algebra of the given type. Using this kernel, we define three relations between sets of hypersubstitutions and sets of varieties and introduce the Galois correspondences induced by these relations. Then we apply these general concepts to varieties of semigroups.
Keywords: hypersubstitution, fully invariant congruence relation, hyperunification problem.
2000 Mathematics Subject Classification: 08B15, 08B25.
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Received 16 March 2001
Revised 8 August 2001