Article ID | Journal | Published Year | Pages | File Type |
---|---|---|---|---|
4585731 | Journal of Algebra | 2012 | 5 Pages |
Abstract
Let 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) [9] by showing that over a right noetherian prime right SI-ring, quasi-projective right modules are projective or semisimple.
Related Topics
Physical Sciences and Engineering
Mathematics
Algebra and Number Theory