On homomorphisms between products of median algebras

Abstract : Homorphisms of products of median algebras are studied with particular attention to the case when the codomain is a tree. In particular, we show that all mappings from a product $\mathbf{A}_1\times \cdots \times \mathbf{A}_n$ of median algebras to a median algebra $\mathbf{B}$ are essentially unary whenever the codomain $\mathbf{B}$ is a tree. In view of this result, we also characterize trees as median algebras and semilattices by relaxing the defining conditions of conservative median algebras.
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Miguel Couceiro, Stephan Foldes, Gerasimos Meletiou. On homomorphisms between products of median algebras. Algebra Universalis, Springer Verlag, 2017, 78 (4), pp.545-553. ⟨10.1007/s00012-017-0468-6⟩. ⟨hal-01500223⟩

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