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INJECTIVE MODULES OVER ω-NOETHERIAN RINGS, II
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 Title & Authors
INJECTIVE MODULES OVER ω-NOETHERIAN RINGS, II
Zhang, Jun; Wang, Fanggui; Kim, Hwankoo;
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 Abstract
By utilizing known characterizations of -Noetherian rings in terms of injective modules, we give more characterizations of -Noetherian rings. More precisely, we show that a commutative ring R is -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 -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 -injective -module is injective; if and only if every GV-torsion-free R-module admits an -decomposition.
 Keywords
GV -torsion-free module;-module;-simple module;-Noetherian ring;injective module;
 Language
English
 Cited by
1.
MODULES SATISFYING CERTAIN CHAIN CONDITIONS AND THEIR ENDOMORPHISMS, Bulletin of the Korean Mathematical Society, 2015, 52, 2, 549  crossref(new windwow)
2.
The Direct and Inverse Limits ofw-Modules, Communications in Algebra, 2016, 44, 6, 2495  crossref(new windwow)
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