1. Open Access Kent State
  2. Quasi-Projective Modules Over Prime Hereditary Noetherian V-rings are Projective or Injective
Author(s)
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) by showing that over a right noetherian prime right SI-ring, quasi-projective right modules are projective or semisimple.
Format
Article
Identifier(s)
10.1016/J.JALGEBRA.2012.04.002
Publication Date
2012-06-01
Publication Title
Elsevier
Volume
360
First Page
87
Last Page
91
Keywords
Subject
Community
Department of Mathematical Sciences
Permalink https://oaks.kent.edu/mathpubs/12
Dinh, H., Holston, C., & Huynh, D. (2012). Quasi-Projective Modules Over Prime Hereditary Noetherian V-rings are Projective or Injective. Elsevier. https://doi.org/10.1016/J.JALGEBRA.2012.04.002
Dinh, Hai, Christopher Holston, and Dinh Huynh. 2012. “Quasi-Projective Modules Over Prime Hereditary Noetherian V-Rings Are Projective or Injective”. Elsevier. https://doi.org/10.1016/J.JALGEBRA.2012.04.002.
Dinh, H., C. Holston, and D. Huynh. Quasi-Projective Modules Over Prime Hereditary Noetherian V-Rings Are Projective or Injective. Elsevier, 1 June 2012, doi:10.1016/J.JALGEBRA.2012.04.002.