### Quasi-Projective Modules Over Prime Hereditary Noetherian V-rings are Projective or Injective

06/01/2012Let **Q** be the field of rational numbers. As a module over the ring **Z** of integers, **Q** is **Z**-projective, but **QZ** is not a projective module. Contrary to this situation, we show that over a prime right noetherian right hereditary right V-ring *R*, a right module *P* is projective if and only if *P* is *R*-projective. As a consequence of this we obtain the result stated in the title. Furthermore, we apply this to affirmatively answer a question that was left open in a recent work of Holston, López-Permouth and Orhan Ertag (2012) by showing that over a right noetherian prime right SI-ring, quasi-projective right modules are projective or semisimple.