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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



Hereditary $ QI$-rings

Author: Ann K. Boyle
Journal: Trans. Amer. Math. Soc. 192 (1974), 115-120
MSC: Primary 16A52
MathSciNet review: 0338075
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Abstract: We consider in this paper rings in which every quasi-injective right R-module is injective. These rings will be referred to as right QI-rings. For a hereditary ring, this is equivalent to the condition that R be noetherian and a right V-ring. We also consider rings in which proper cyclic right R-modules are injective. These are right QI-rings which are either semisimple or right hereditary, right Ore domains in which indecomposable injective right R-modules are either simple or isomorphic to the injective hull of $ {R_R}$.

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Keywords: Right V-ring, simple module, hereditary ring, QI-ring, quasi-injective module, injective module, torsion module, proper cyclic, PCI-ring
Article copyright: © Copyright 1974 American Mathematical Society