Abstract
An endomorphism on an algebra $${\mathcal {A}}$$ is said to be strong if it is compatible with every congruence on $${\mathcal {A}}$$ ; and $${\mathcal {A}}$$ is said to have the strong endomorphism kernel property if every congruence on $${\mathcal {A}}$$ , other than the universal congruence, is the kernel of a strong endomorphism on $${\mathcal {A}}$$ . Here we characterise the structure of Ockham algebras with balanced pseudocomplementation those that have this property via Priestley duality.
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