Modular Classes of Poisson–Nijenhuis Lie Algebroids

The modular vector field of a Poisson–Nijenhuis Lie algebroid A is defined and we prove that, in case of non-degeneracy, this vector field defines a hierarchy of bi-Hamiltonian A-vector fields. This hierarchy covers an integrable hierarchy on the base manifold, which may not have a Poisson–Nijenhuis structure.