# Can I make the correspondence theorem for rings similar to that of the one for groups?

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?

• – Joel Pereira Oct 22 '18 at 4:07