Matrix rings with summand intersection property
A ring has right SIP (SSP) if the intersection (sum) of two direct summands of 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 by has SIP if and only if has SIP and for every idempotent in . Moreover, we give necessary and sufficient conditions for the generalized upper triangular matrix rings to have SIP.