Abstract
Homomorphisms 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 \({\mathbf{A_1} \times\ldots\times {\mathbf{A}_{n}}}\) 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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Presented by M. Jackson.
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Couceiro, M., Foldes, S. & Meletiou, G.C. On homomorphisms between products of median algebras. Algebra Univers. 78, 545–553 (2017). https://doi.org/10.1007/s00012-017-0468-6
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DOI: https://doi.org/10.1007/s00012-017-0468-6