Excellent Extensions and Global Cotorsion Dimensions
نویسندگان
چکیده
منابع مشابه
Gorenstein Global Dimensions and Cotorsion Dimension of Rings
In this paper, we establish, as a generalization of a result on the classical homological dimensions of commutative rings, an upper bound on the Gorenstein global dimension of commutative rings using the global cotorsion dimension of rings. We use this result to compute the Gorenstein global dimension of some particular cases of trivial extensions of rings and of group rings.
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Let $Gamma$ be a group, $Gamma'$ a subgroup of $Gamma$ with finite index and $M$ be a $Gamma$-module. We show that $M$ is cotorsion if and only if it is cotorsion as a $Gamma'$-module. Using this result, we prove that the global cotorsion dimensions of rings $ZGamma$ and $ZGamma'$ are equal.
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Article history: Received 31 December 2010 Available online 14 March 2012 Communicated by Luchezar L. Avramov MSC: 16G10 16G60 16S20
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Let R be a subring of the rationals. We want to investigate self splitting R-modules G that is ExtR(G,G) = 0 holds and follow Schultz [22] to call such modules splitters. Free modules and torsion-free cotorsion modules are classical examples for splitters. Are there others? Answering an open problem by Schultz [22] we will show that there are more splitters, in fact we are able to prescribe the...
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ژورنال
عنوان ژورنال: Tokyo Journal of Mathematics
سال: 2012
ISSN: 0387-3870
DOI: 10.3836/tjm/1342701341