Let's consider the $N$-th root $\xi$ of unity and the ring $Z_N$ of the numbers of the form $p + q\xi$ with $p,q\in \mathbb{Z}$. I am interested in the ideals of $Z_N$ when $N$ is even and $N \ge 4$. Spelling this out should be redundant with my title, I know, but I am not a specialist at all, coming at this from physics, and I want to make sure I am not misusing the terminology. From hand made scribblings, I am pretty convinced every ideal is principal for $N = 4, 6, 8, 10$. My question is then: what is known for higher values of $N$? I have the feeling that there must be non-principal ideals but what is the smallest value of $N$ for that to happen?
2026-03-25 23:52:24.1774482744
Principal ideals of integers ring of cyclotomic field
333 Views Asked by user450847 https://math.techqa.club/user/user450847/detail AtRelated Questions in IDEALS
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