# contracted ideal

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

Title contracted ideal ContractedIdeal 2013-03-22 12:55:31 2013-03-22 12:55:31 drini (3) drini (3) 5 drini (3) Definition msc 13A15 msc 14K99 msc 16D25 ExtendedIdeal