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http://dx.doi.org/10.4134/JKMS.2013.50.5.1051

INJECTIVE MODULES OVER ω-NOETHERIAN RINGS, II  

Zhang, Jun (Institute of Mathematics and Software Science School of Foreign Languages Sichuan Normal University)
Wang, Fanggui (Institute of Mathematics and Software Science Sichuan Normal University)
Kim, Hwankoo (Department of Information Security Hoseo University)
Publication Information
Journal of the Korean Mathematical Society / v.50, no.5, 2013 , pp. 1051-1066 More about this Journal
Abstract
By utilizing known characterizations of ${\omega}$-Noetherian rings in terms of injective modules, we give more characterizations of ${\omega}$-Noetherian rings. More precisely, we show that a commutative ring R is ${\omega}$-Noetherian if and only if the direct limit of GV -torsion-free injective R-modules is injective; if and only if every R-module has a GV -torsion-free injective (pre)cover; if and only if the direct sum of injective envelopes of ${\omega}$-simple R-modules is injective; if and only if the essential extension of the direct sum of GV -torsion-free injective R-modules is the direct sum of GV -torsion-free injective R-modules; if and only if every $\mathfrak{F}_{w,f}(R)$-injective ${\omega}$-module is injective; if and only if every GV-torsion-free R-module admits an $i$-decomposition.
Keywords
GV -torsion-free module; ${\omega}$-module; ${\omega}$-simple module; ${\omega}$-Noetherian ring; injective module;
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Times Cited By KSCI : 2  (Citation Analysis)
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