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Abstract
An algebra 𝒜 has the endomorphism kernel property if every congruence on 𝒜 different from the universal congruence is the kernel of an endomorphism on 𝒜. We first consider this property when 𝒜 is a finite distributive lattice, and show that it holds if and only if 𝒜 is a cartesian product of chains. We then consider the case where 𝒜 is an Ockham algebra, and describe in particular the structure of the finite de Morgan algebras that have this property.
1991 Mathematics Subject Classification:
Acknowledgments
The authors are indebted to Professor Brian Davey who, on reading an earlier version of this paper, made valuable suggestions which have acted as a catalyst in the evolution of Theorem 3.
The second author expresses his gratitude to the Centro de Matemática e Aplicações, F.C.T., Universidade Nova de Lisboa where part of this research was carried out.
Notes
#Communicated by P. Higgins.