The Endomorphism Kernel Property in Finite Distributive Lattices and de Morgan Algebras

An algebra has the endomorphism kernel property if every congruence on different from the universal congruence is the kernel of an endomorphism on . We first consider this property when is a finite distributive lattice, and show that it holds if and only if is a cartesian product of chains. We then...

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Bibliographic Details
Published in:Communications in algebra 2004-12, Vol.32 (6), p.2225-2242
Main Authors: Blyth, T. S., Fang, J., Silva, H. J.
Format: Article
Language:English
Subjects:
de Morgan algebra
Endomorphism kernel
Kleene algebra
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Summary:An algebra has the endomorphism kernel property if every congruence on different from the universal congruence is the kernel of an endomorphism on . We first consider this property when is a finite distributive lattice, and show that it holds if and only if is a cartesian product of chains. We then consider the case where is an Ockham algebra, and describe in particular the structure of the finite de Morgan algebras that have this property.
ISSN:0092-7872
1532-4125
DOI:10.1081/AGB-120037216