Strong endomorphism kernel property for monounary algebras
Strong endomorphism kernel property for monounary algebras
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.
connected monounary algebra, cycle, strong endomorphism, kernel, congruence, (strong) endomorphism, QA1-939, Unary algebras, Automorphisms and endomorphisms of algebraic structures, Subalgebras, congruence relations, Mathematics
connected monounary algebra, cycle, strong endomorphism, kernel, congruence, (strong) endomorphism, QA1-939, Unary algebras, Automorphisms and endomorphisms of algebraic structures, Subalgebras, congruence relations, Mathematics
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