Matrix rings with summand intersection property

Karabacak F., Tercan A.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.53, no.3, pp.621-626, 2003 (Peer-Reviewed Journal) identifier identifier

  • Publication Type: Article / Article
  • Volume: 53 Issue: 3
  • Publication Date: 2003
  • Doi Number: 10.1023/b:cmaj.0000024507.03939.ce
  • Journal Indexes: Science Citation Index Expanded, Scopus
  • Page Numbers: pp.621-626


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.