# Image of Ideal under Ring Epimorphism is Ideal

 It has been suggested that this page or section be merged into Ring Epimorphism Preserves Ideals. (Discuss)

## Theorem

Let $f : A \to B$ be a ring epimorphism.

Let $I \subseteq A$ be an ideal.

Then its image $f(I) \subseteq B$ is an ideal.