Countable injective modules are sigma injective
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- by Charles Megibben PDF
- Proc. Amer. Math. Soc. 84 (1982), 8-10 Request permission
Abstract:
In this note we show that a countable injective module is $\sum$-injective and consequently a ring $R$ is left noetherian if the category of left $R$-modules has a countable injective cogenerator. Our proof can be modified to establish the corresponding result for quasi-injective modules. We also give an example of a nonnoetherian commutative ring $R$ such that the category of $R$-modules has a countable cogenerator.References
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Additional Information
- © Copyright 1982 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 84 (1982), 8-10
- MSC: Primary 16A52; Secondary 16A33
- DOI: https://doi.org/10.1090/S0002-9939-1982-0633266-2
- MathSciNet review: 633266