Geodesic
Matrix rings with summand intersection property
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 621-626
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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.
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.
Classification : 16D10, 16D15, 16D70, 16S50
Keywords: modules; Summand Intersection Property; Morita invariant 
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}
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Karabacak, F.; Tercan, A. Matrix rings with summand intersection property. Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 621-626. http://geodesic.mathdoc.fr/item/CMJ_2003_53_3_a9/

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