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Proceedings of the American Mathematical Society

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

 
 

 

On splitting cotorsion radicals


Author: V. S. Ramamurthi
Journal: Proc. Amer. Math. Soc. 39 (1973), 457-461
MSC: Primary 16A62
DOI: https://doi.org/10.1090/S0002-9939-1973-0313323-5
MathSciNet review: 0313323
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Abstract: For a category of modules, the notion, dual to that of a torsion radical, has been called a cotorsion radical. In this paper, the following two properties are examined for a cotorsion radical $ \rho $: (1) If $ N$ is a submodule of $ M$ and $ \rho (M) = M$, then $ \rho (N) = N$. (2) The exact sequence $ 0 \to \rho (M) \to M \to M/\rho (M) \to 0$ splits for each module $ M$.


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DOI: https://doi.org/10.1090/S0002-9939-1973-0313323-5
Keywords: Torsion radical, cotorsion radical, flat modules, von Neumann regular rings, semiperfect rings, quasi-Frobenius ring
Article copyright: © Copyright 1973 American Mathematical Society

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