Suppose $I$ is an ideal of ring $R$, and $J'$ is an ideal of $R/I$. Show there is an ideal $J$ in $R$ so that $J/I=J'$.
How do I answer this? What am I required to prove?
2026-04-13 06:14:42.1776060882
Rings, ideals and quotient rings
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There is a canonical map $\varphi : R \to R/I$. You want an ideal $J$ in $R$ so that $\varphi(J)=J'$. You answer this by finding the ideal and proving it satisfies that condition.