Generalized hereditary Noetherian prime rings


Akalan E., Marubayashi H., Ueda A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.17, 2018 (SCI İndekslerine Giren Dergi) identifier identifier

  • Cilt numarası: 17 Konu: 8
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1142/s0219498818501530
  • Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS

Özet

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.