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Title: Matrix rings with summand intersection property (English)
Author: Karabacak, F.
Author: Tercan, A.
Language: English
Journal: Czechoslovak Mathematical Journal
ISSN: 0011-4642 (print)
ISSN: 1572-9141 (online)
Volume: 53
Issue: 3
Year: 2003
Pages: 621-626
Summary lang: English
Category: math
Summary: 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. (English)
Keyword: modules
Keyword: Summand Intersection Property
Keyword: Morita invariant
MSC: 16D10
MSC: 16D15
MSC: 16D70
MSC: 16S50
idZBL: Zbl 1080.16503
idMR: MR2000057
Date available: 2009-09-24T11:05:01Z
Last updated: 2020-07-03
Stable URL:
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