Geodesic
Matrix rings with summand intersection property
Czechoslovak Mathematical Journal, Tome 53 (2003) no. 3, pp. 621-626 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 
@article{CMJ_2003_53_3_a9,
     author = {Karabacak, F. and Tercan, A.},
     title = {Matrix rings with summand intersection property},
     journal = {Czechoslovak Mathematical Journal},
     pages = {621--626},
     year = {2003},
     volume = {53},
     number = {3},
     mrnumber = {2000057},
     zbl = {1080.16503},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/CMJ_2003_53_3_a9/}
}
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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/