The p.p. property of trivial extensions
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, cilt.14, sa.8, 2015 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 14 Sayı: 8
- Basım Tarihi: 2015
- Doi Numarası: 10.1142/s0219498815501248
- Dergi Adı: JOURNAL OF ALGEBRA AND ITS APPLICATIONS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: Left p.p.-ring, formal triangular matrix ring, trivial Morita context, trivial extension, MORITA CONTEXTS
- Gazi Üniversitesi Adresli: Hayır
Özet
In this note, a necessary and sufficient condition for a trivial extension to be a left p.p.-ring is obtained. As an application, we determine when a trivial Morita context is a left p.p.-ring, and a result of Xue [On p.p. rings, Kobe J. Math. 7 (1990) 77-80] characterizing triangular p.p.-rings follows immediately.