Definition:Contraction of Ideal

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Definition

Let $A$ and $B$ be commutative ring with unity.

Let $f : A \to B$ be a ring homomorphism.

Let $\mathfrak b \subseteq B$ be an ideal.


The contraction of $\mathfrak b$ by $f$ is its preimage under $f$:

$\mathfrak b^c = f^{-1}(\mathfrak b)$


Also see


Sources