I have no idea how to answer this question.
Let R be the quotient ring $\mathbb Q[X]/(X^3 + X^2 + X + 1)$. How to list all the ideals of R? And how to determine whether each ideal is prime, maximal, or neither?
2026-04-24 03:51:14.1777002674
Listing all the ideals of a quotient ring
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Hint: $\mathbb Q$ is a field so $\mathbb Q[x]$ is a PID. What does the correspondence theorem say about ideals and what does that translate to when the ideals are principal?