Correspondence Theorem for Quotient Rings

Theorem
Let $A$ be a commutative ring with unity.

Let $\mathfrak a \subseteq A$ be an ideal.

Let $A/\mathfrak a$ be the quotient ring and $\pi : A \to A/\mathfrak a$ the quotient mapping.

Generalization

 * Correspondence Theorem for Surjective Ring Homomorphisms