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.
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Dedicated to George Grätzer and E. Tamás Schmidt on their 70th birthdays
The first author was supported by Slovak VEGA Grant 1/0423/23, the second author by VEGA grant 1/3026/06 and by grant APVV-51-009605.
Received November 21, 2006; accepted in final form November 6, 2007.
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Ploščica, M., Haviar, M. Congruence-preserving functions on distributive lattices. Algebra univers. 59, 179–196 (2008). https://doi.org/10.1007/s00012-008-2099-4
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DOI: https://doi.org/10.1007/s00012-008-2099-4