## Weak homomorphisms in implication algebra.(English)Zbl 0703.08002

Let $${\mathfrak A}=<A,F>$$, $${\mathfrak B}=<B,G>$$ be algebras. A mapping h: $$A\to B$$ is called a semi-weak homomorphism if for each n-ary operation $$f\in F$$ there is an n-ary term g of $${\mathfrak B}$$ such that $$h(f(a_ 1,...,a_ n))=g(h(a_ 1),...,h(a_ n))$$ for any $$a_ 1,...,a_ n\in A$$. It is proven that the only surjective semi-weak homomorphisms of implication algebras are the usual homomorphisms.
Reviewer: J.Duda

### MSC:

 08A35 Automorphisms and endomorphisms of algebraic structures 06A12 Semilattices

### Keywords:

semi-weak homomorphism; implication algebras
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