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

Blyth, Tom S.; Fang, Jie; Wang, Lei-Bo

Sci. Math. Jpn. 76, No. 2, 227-234 (2013).

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)

Keywords:

strong endomorphism kernel property; double \(p\)-algebras; strong endomorphisms; congruences