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Rings whose quasi-injective modules are injective


Author: K. A. Byrd
Journal: Proc. Amer. Math. Soc. 33 (1972), 235-240
MSC: Primary 16A52
DOI: https://doi.org/10.1090/S0002-9939-1972-0310009-7
MathSciNet review: 0310009
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Abstract: A ring R is called a V-ring, respectively SSI-ring, respectively QII-ring if simple, respectively semisimple, respectively quasi-injective, right R-modules are injective. We show that R is SSI if and only if R is a right noetherian V-ring and that any SSI-ring is a finite ring direct sum of simple SSI-rings. We show that if R is left noetherian and SSI then R is QII provided R is hereditary and that in order for R to be hereditary it suffices that maximal right ideals of R be reflexive. An example of Cozzens is cited to show these rings need not be artinian.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0310009-7
Keywords: Quasi-injective module, V-ring, Morita-equivalent, quotient ring
Article copyright: © Copyright 1972 American Mathematical Society

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