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**cristianoceli** Hi! I have problems with this demostration

Let $\displaystyle I$ be an ideal in a commutative ring $\displaystyle R$. If $\displaystyle J$ is an ideal in $\displaystyle R$ and $\displaystyle I\subseteq{J}$, prove that: $\displaystyle J/I = \{ r+I : r \in{J} \} $ is an ideal in $\displaystyle R/I$

Demostration

If $\displaystyle J+I\in J/I$, then $\displaystyle J+I\in R/I$ because $\displaystyle J\subset R$, therefore $\displaystyle J/I\subset R/I$.

Is the demonstration correct?