Extension and contraction of ideals
= Extension and contraction of ideals
For a <ring homomorphism> $f:R\to S$, extension sends an <ideal> $I\subseteq R$ to the ideal $S f(I)$ generated by its image. Contraction sends an ideal $J\subseteq S$ to $f^{-1}(J)$. These are distinct forward and inverse-image operations.