Definition:Ring Extension

Definition
Let $R$ and $S$ be rings.

Let $\phi : R \to S$ be an injective homomorphism of rings.

Then $\phi : R \to S$ is a ring extension of $R$.

When $R \subseteq S$ is a subring, one often omits explicit reference to the homomorphism $\phi$ and writes $S/R$ or $R \leq S$.

Also See

 * Field extension