On splitting cotorsion radicals

Ramamurthi, V. S.

doi:10.1090/S0002-9939-1973-0313323-5

On splitting cotorsion radicals
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by V. S. Ramamurthi

Proc. Amer. Math. Soc. 39 (1973), 457-461

DOI: https://doi.org/10.1090/S0002-9939-1973-0313323-5

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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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