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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 

 

Rings of equivalent dominant and codominant dimensions


Author: Gary L. Eerkes
Journal: Proc. Amer. Math. Soc. 48 (1975), 297-306
DOI: https://doi.org/10.1090/S0002-9939-1975-0360710-7
MathSciNet review: 0360710
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Abstract | References | Additional Information

Abstract: Continuing an earlier examination of the codominant dimension of rings and modules, a categorical characterization is given for rings of equivalent dominant and codominant dimensions. Specifically, the question is reduced to when $ {}_RR$ and the left minimal injective cogenerator $ {}_R\mathcal{U}$ can be used as test modules respectively for the dominant dimension of the projective modules and the codominant dimension of the injective modules. These conditions are in turn characterized by when the injective projective modules are $ \mathbf{\Sigma }$-injective. Also, a new and shortened version is given for the proof that the codominant dimension of the injective modules is equal to the dominant dimension of the projective modules.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1975-0360710-7
Keywords: Perfect rings, injective projective modules, codominant and dominant dimensions, $ \mathbf{\Sigma }$-injectivity
Article copyright: © Copyright 1975 American Mathematical Society