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The entanglement-sharing properties of an infinite spin-chain are studiedwhen the state of the chain is a pure, translation-invariant state with amatrix-product structure. We study the entanglement properties of such statesby means of their finitely correlated structure. These states are recursivelyconstructed by means of an auxiliary density matrix \rho on a matrix algebra Band a completely positive map E: A \otimes B -> B, where A is the spin 2\times2 matrix algebra. General structural results for the infinite chain aretherefore obtained by explicit calculations in (finite) matrix algebras. Inparticular, we study not only the entanglement shared by nearest-neighbours,but also, differently from previous works, the entanglement shared betweenconnected regions of the spin-chain. This range of possible applications isillustrated and the maximal concurrence C=1/\sqrt{2} for the entanglement ofconnected regions can actually be reached.Comment: 7 pages, 2 figures, to be published in Eur.Phys.Let

Multi-distributed entanglement in finitely correlated chains