Moderate# Isomorphism Theorems (Rings): Applying Fourth Isomorphism Theorem

ABSALG-GAJLON

Let $R$ be a ring and $\mathfrak{A}$ an ideal of $R$.

The **Fourth Isomorphism Theorem for Rings** states that there is a bijection between:

{The ideals $\mathfrak{B}$ of $R$ containing $\mathfrak{A}$} and {The ideals of $R/\mathfrak{A}$} given by $\mathfrak{B}\mapsto \mathfrak{B/A}$

This theorem is also often called the **Correspondence Theorem for Rings**.

Which of the following is **false**?