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The strong endomorphism kernel property in distributive double \(p\)-algebras. (English) Zbl 1320.06009

Summary: An endomorphism of 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 describe, by way of Priestley duality, the distributive double \(p\)-algebras that have the strong endomorphism kernel property.

MSC:

06D15 Pseudocomplemented lattices
08A30 Subalgebras, congruence relations
08A35 Automorphisms and endomorphisms of algebraic structures
06D30 De Morgan algebras, Łukasiewicz algebras (lattice-theoretic aspects)
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