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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
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Category: math
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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
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Date available: 2009-09-24T11:05:01Z
Last updated: 2016-04-07
Stable URL: http://hdl.handle.net/10338.dmlcz/127827
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Reference: [3] J. L.  Garcia: Properties of direct summands of modules.Comm. Algebra 17 (1989), 73–92. Zbl 0659.16016, MR 0970864, 10.1080/00927878908823714
Reference: [4] K. R.  Goodearl: Ring Theory.Marcel Dekker, 1976. Zbl 0336.16001, MR 0429962
Reference: [5] J.  Hausen: Modules with the summand intersection property.Comm. Algebra 17 (1989), 135–148. Zbl 0667.16020, MR 0970868, 10.1080/00927878908823718
Reference: [6] I.  Kaplansky: Infinite Abelian Groups.University of Michigan Press, 1969. Zbl 0194.04402, MR 0233887
Reference: [7] G. V.  Wilson: Modules with the summand intersection property.Comm. Algebra 14 (1986), 21–38. Zbl 0592.13008, MR 0814137, 10.1080/00927878608823297
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