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 $\mathfrak b$ be an ideal of $B$.
The contraction of $\mathfrak b$ by $f$ is its preimage under $f$:
- $\mathfrak b^c = f^{-1} \sqbrk {\mathfrak b}$
Also see
Sources
- 1969: M.F. Atiyah and I.G. MacDonald: Introduction to Commutative Algebra ... (previous): Chapter $1$: Rings and Ideals: $\S$ Extension and Contraction