Matrix rings with summand intersection property
CZECHOSLOVAK MATHEMATICAL JOURNAL, cilt.53, sa.3, ss.621-626, 2003 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 53 Sayı: 3
- Basım Tarihi: 2003
- Doi Numarası: 10.1023/b:cmaj.0000024507.03939.ce
- Dergi Adı: CZECHOSLOVAK MATHEMATICAL JOURNAL
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Sayfa Sayıları: ss.621-626
- Açık Arşiv Koleksiyonu: AVESİS Açık Erişim Koleksiyonu
- Hacettepe Üniversitesi Adresli: Hayır
Özet
A ring R has right SIP (SSP) if the intersection (sum) of two direct summands of R is also a direct summand. We show that the right SIP (SSP) is the Morita invariant property. We also prove that the trivial extension of R by M has SIP if and only if R has SIP and (1 - e)Me = 0 for every idempotent e in R. Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.