Finitely Projective Modules over Bounded Hereditary Noetherian Prime Rings

The author has studied in [10] finitely projective modules over Dedekind domains. In this paper we generalize the results of [10] to finitely projective modules over bounded hereditary. Noetherian prime rings. Our main theorem asserts that if R is a bounded hereditary Noetherian prime ring then a right R-module is finitely projective if and only if its reduced part is torsionless and coseparable. The finite projectivity is a pure-hereditary property for modules over bounded hereditary Noetherian prime rings. We also prove that if is a right bounded, right Noetherian, prime, left Goldie ring then every finitely projective right - R-module is projective if and only if R equals its two-sided classical quotient ring.