Strong endomorphism kernel property for monounary algebras. (English) Zbl 1463.08003

An endomorphism of an algebra \(A\) is called strong if it is compatible with all congruences on \(A\). If every congruence on \(A\) is a kernel of some strong endomorphism, then \(A\) is said to have a strong endomorphism kernel property (SEKP for short). If in this definition we exclude the universal congruence \(A^2\), then this weaker property is denoted by wSEKP. The author characterizes all monounary algebras having SEKP and those having wSEKP.


08A30 Subalgebras, congruence relations
08A35 Automorphisms and endomorphisms of algebraic structures
08A60 Unary algebras
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