Discussiones
Mathematicae General Algebra and Applications 21(2) (2001)175-200
doi: 10.7151/dmgaa.1036
Klaus Denecke, Jörg Koppitz University of Potsdam, Institute of Mathematics, |
Shelly Wismath Department of Mathematics and C.S., University of
Lethbridge, |
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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[2] | K. Denecke, J. Koppitz and St. Niwczyk, Equational Theories generated by Hypersubstitutions of Type (n), Internat. J. Algebra Comput., in print. |
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[4] | K. Denecke and S.L. Wismath, Hyperidentities and Clones, Gordon and Breach Sci. Publ., Amsterdam 2000. |
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[6] | J.H. Siekmann, Universal Unification, p. 1-42 in: Lecture Notes in Computer Science, no. 170 (``International Conference on Automated Deductions (Napa, CA, 1984)"), Springer-Verlag, Berlin 1984. |
Received 16 March 2001
Revised 8 August 2001