## Semilattices with the strong endomorphism kernel property.(English)Zbl 1305.06004

By a strong endomorphism on an algebra $$A$$ is meant an endomorphism which is compatible with every congruence on $$A$$. An algebra $$A$$ has the strong endomorphism kernel property if every congruence on $$A$$ other than the universal congruence, is the kernel of a strong endomorphism on $$A$$. There are characterized strong endomorphisms on meet semilattices and it is shown that a semilattice has the strong endomorphism kernel property if and only if either it is of length 1 or it has length 2 and contains a monolith.

### MSC:

 06A12 Semilattices 08A35 Automorphisms and endomorphisms of algebraic structures
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### References:

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