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 ${𝔟}^c$.

Title	contracted ideal
Canonical name	ContractedIdeal
Date of creation	2013-03-22 12:55:31
Last modified on	2013-03-22 12:55:31
Owner	drini (3)
Last modified by	drini (3)
Numerical id	5
Author	drini (3)
Entry type	Definition
Classification	msc 13A15
Classification	msc 14K99
Classification	msc 16D25
Related topic	ExtendedIdeal