Kernel of a ring homomorphism
= Kernel of a ring homomorphism
{title2=$\ker\varphi$}
The kernel of a <ring homomorphism> $\varphi:R\to S$ is the <ideal> $\{r\in R:\varphi(r)=0\}$. The <ring homomorphism> is <injective> exactly when this <ideal> is zero.