0
$\begingroup$

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?

$\endgroup$
1
  • $\begingroup$ Another hint: $1+x+x^2+x^3=(x^4-1)/(x-1)$. $\endgroup$
    – Fredrik Meyer
    Apr 15, 2016 at 13:55

1 Answer 1

Reset to default
2
$\begingroup$

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?

$\endgroup$

Not the answer you're looking for? Browse other questions tagged .