I am trying to show that
(R/I)/(J/I) is isomorphic to R/J
I and J are both ideals of the ring R, and I is a subset of J.
How do I begin this proof?
2026-04-12 03:32:03.1775964723
Ideals and quotient rings
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There are 1 best solutions below
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Hint:
Define
$$\phi:R/I\to R/J\;\;,\;\;\phi(r+I):=r+J$$
Show this is a well defined function (i.e., $\;r+I=r'+I\implies r+J=r'+J\;$) and that it is an onto ring homomorphism. Now, what is its kernel? And then use the first isomorphism theorem.