Generalized hereditary Noetherian prime rings

Akalan E., Marubayashi H., Ueda A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, vol.17, no.8, 2018 (SCI-Expanded) identifier identifier


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.