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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Rings of equivalent dominant and codominant dimensions
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by Gary L. Eerkes PDF
Proc. Amer. Math. Soc. 48 (1975), 297-306 Request permission

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.
References
Additional Information
  • © Copyright 1975 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 48 (1975), 297-306
  • DOI: https://doi.org/10.1090/S0002-9939-1975-0360710-7
  • MathSciNet review: 0360710