Generalized hereditary Noetherian prime rings
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.17, no.8, 2018 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 17 Issue: 8
- Publication Date: 2018
- Doi Number: 10.1142/s0219498818501530
- Journal Name: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Hacettepe University Affiliated: Yes
Abstract
The polynomial rings over hereditary Noetherian prime rings have global dimension 2 and any two-sided ideal which is either left v-ideal or right v-ideal is left and right projective. By using the latter property, we define the concept of generalized hereditary Noetherian prime rings (G-HNP rings). We study the structure of projective ideals in G-HNP rings and some overrings of G-HNP rings. As it is shown in the examples, the class of G-HNP rings ranges from rings with global dimension 2 to rings with infinite global dimension and Noetherian prime rings with global dimension 2 are not necessarily G-HNP rings.