Matrix rings with summand intersection property
CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.53, no.3, pp.621-626, 2003 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 53 Issue: 3
- Publication Date: 2003
- Doi Number: 10.1023/b:cmaj.0000024507.03939.ce
- Journal Name: CZECHOSLOVAK MATHEMATICAL JOURNAL
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.621-626
- Open Archive Collection: AVESIS Open Access Collection
- Hacettepe University Affiliated: No
Abstract
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.