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Let $R$ be a commutative ring and $I,J,K$ be ideals such that $I\subseteq J$ and $I\subseteq K$.

Let $\pi: R \to R/I$ be the canonical map. I am able to prove $\pi$ preserves sum and products. Unsure about intersections.

$J/I + K/I = (J+K)/I$

$J/I \cdot K/I = (J\cdot K)/I$

$J/I \cap K/I = (J\cap K)/I$?

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