The Endomorphism Kernel Property in Finite Distributive Lattices and de Morgan Algebras
T. S. Blyth, Jie Fang, H. J. Silva Β· Communications in Algebra Β· 2004
An algebra π has the endomorphism kernel property if every congruence on π different from the universal congruence is the kernel of an endomorphism on π. We first consider this property when π is a finite distributive lattice, and show that it holds if and only if π is a cartesian product of chains. We then consider the case where π is an Ockham algebra, and describe in particular the structure of the finite de Morgan algebras that have this property.