Hereditary 𝑄𝐼-rings

Boyle, Ann K.

doi:10.1090/S0002-9947-1974-0338075-X

Hereditary $QI$-rings
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by Ann K. Boyle PDF

Trans. Amer. Math. Soc. 192 (1974), 115-120 Request permission

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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