Finitely Projective Modules over Bounded Hereditary Noetherian Prime Rings
The author has studied in  finitely projective modules over Dedekind domains. In this paper we generalize the results of  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.
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