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Algebra universalis

, Volume 59, Issue 1–2, pp 179–196 | Cite as

Congruence-preserving functions on distributive lattices

  • Miroslav Ploščica
  • Miroslav Haviar
Article

Abstract.

This paper is a continuation of the research motivated by G. Grätzer’s study of affine completeness for Boolean algebras and distributive lattices from 1962 and 1964, respectively and by the 1995 work of G. Grätzer and E. T. Schmidt on unary isotone congruence-preserving functions of distributive lattices. We present a complete list of generators for the clone C(L) of all congruence-preserving functions of any distributive lattice L. We introduce a general problem of finding a nice generating set for the clone C(A) of all congruence-preserving functions of a given algebra A.

2000 Mathematics Subject Classification:

06D15 08A40 

Keywords and phrases:

distributive lattice congruence compatible function polynomial 

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Copyright information

© Birkhaueser 2008

Authors and Affiliations

  1. 1.Faculty of Natural SciencesŠafárik UniversityKošiceSlovakia
  2. 2.Mathematical InstituteSlovak Academy of SciencesKošiceSlovakia
  3. 3.Department of Mathematics, Pedagogic FacultyMatej Bel UniversityBanská BystricaSlovakia
  4. 4.Institute for Science and ResearchMatej Bel UniversityBanská BystricaSlovakia

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