contracted ideal

Let $f:A\to B$ be a ring homomorphism. Let $𝔟$ be an ideal in $B$. Then it is easy to show that the inverse image of $𝔟$, that is $f^{-1}(𝔟)$, is an ideal in $A$, and we call it a contracted ideal. A common notation for the contracted ideal in this case is ${𝔟}^c$.