Matrix rings with summand intersection property

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Karabacak F., Tercan A.

CZECHOSLOVAK MATHEMATICAL JOURNAL, vol.53, no.3, pp.621-626, 2003 (SCI-Expanded) identifier identifier


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.