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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
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