Generalized hereditary Noetherian prime rings

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Atıf İçin Kopyala

Akalan E., Marubayashi H., Ueda A.

JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.17, sa.8, 2018 (SCI-Expanded)

• Yayın Türü: Makale / Tam Makale
• Cilt numarası: 17 Sayı: 8
• Basım Tarihi: 2018
• Doi Numarası: 10.1142/s0219498818501530
• Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
• Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
• Hacettepe Üniversitesi Adresli: Evet

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.