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I tried to follow the correspondence theorem for groups to write out the correspondence theorem for rings.

Let $I$ be an ideal in a ring $R$. Then there exists a one-to-one correspondence (a bijection) $S \mapsto S/I$ that corresponds the set of subrings $S$ of $R$ that contain $I$ to the set of subrings $S/I$ of $R/I$.

Is this a correct version of the correspondence theorem?

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