Hi! I have problems with this demostration
Let be an ideal in a commutative ring . If is an ideal in and , prove that:
is an ideal in
Demostration
If , then because , therefore .
Is the demonstration correct?
By Demostration I must assume that you mean PROOF.
You ask: Is the demonstration correct?
That depends upon what is required. What you have posted is correct under certain conditions.
We have no way of knowing what your lecturer requires as a proof.
For me, I expect a student to demonstrate that all conditions for $J/I$ to be an ideal in $R/I$ are meet.
Have you done that?