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Rational Lax hierarchies introduced by Krichever are generalized. Asystematic construction of infinite multi-Hamiltonian hierarchies and relatedconserved quantities is presented. The method is based on the classicalR-matrix approach applied to Poisson algebras. A proof, that Poisson operatorsconstructed near different points of Laurent expansion of Lax functions areequal, is given. All results are illustrated by several examples.Comment: 28 page

Meromorphic Lax representations of (1+1)-dimensional multi-Hamiltonian dispersionless systems