I'm having trouble working this "if and only if", could someone help me?
How to prove that an $R$-module $E$ is injective if and only if for every ideal $I$ of $R$ the short exact sequence $0 \to E \to B \to I \to 0$ splits ?
I'm having trouble working this "if and only if", could someone help me?
How to prove that an $R$-module $E$ is injective if and only if for every ideal $I$ of $R$ the short exact sequence $0 \to E \to B \to I \to 0$ splits ?
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