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The η-meson production in proton-nucleus(pA)collisions near threshold is studied within a relativistic meson-exchange model.The primary production amplitude is presented in the distorted-wave impulse approximation for the nucleus with isospin 0 or [1]by assuming that N*(1535)is excited via a meson exchange and then decays into η and nucleon pair(ηN).Taking 18O and 12C nuclei as examples,we evaluate the production cross sections as a function of the incident proton energy,and analyze the effects of nuclear medium and various meson-exchange contributions.Finally we discuss implications for further experimental studies at the Cooling Storage Ring(CSR)in Lanzhou.