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[en] In this paper we consider nucleus-nucleus and hadron-nucleus reactions in the kinematic region: gA1/3G3Pexp(ΔPY)≥1 and G3P2exp(ΔPY)<1, where G3P is the triple Pomeron coupling, g is the vertex of Pomeron nucleon interaction, and 1+ΔP denotes the Pomeron intercept. We find that in this kinematic region the traditional Glauber-Gribov eikonal approach is inadequate. We show that it is necessary to take into account inelastic Glauber corrections, which cannot be expressed in terms of the nucleon-nucleon scattering amplitudes. We derive the nucleus-nucleus scattering amplitude in the wide range of energies where αP'Y<< RA2, where this amplitude does not depend on the details of the nucleon-nucleon interaction at high energy. In the formalism we present, the only (correlated) parameters that are required to describe the data are ΔP, G3P and g. These parameters were taken from our description of the nucleon-nucleon data at high energies Gotsman et al. (2008) . The predicted nucleus modification factor is compared with RHIC Au-Au data at W=200 GeV. Estimates for LHC energies are presented and discussed.