 Coefficientwise quotient of a polynomial ring (source code)

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= Coefficientwise quotient of a polynomial ring

For an ideal $I$ of a commutative ring $R$, reducing coefficients modulo $I$ is a surjection $R[X]\to(R/I)[X]$ with kernel $I[X]$. Hence
$$
R[X]/I[X]\cong(R/I)[X].
$$

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