Talk:Monogenic field

+1 reference

Corps de nombres algébriques d'anneau d'entiers monogène

Kálmán Györy

Séminaire Delange-Pisot-Poitou. Théorie des nombres (1978-1979)

Volume: 20, Issue: 2, page 1-7

https://eudml.org/doc/111038

Anne Bauval (talk) 13:44, 8 February 2015 (UTC)

Actually even radical extension can be non-monogenic

I have the impression that $\mathbb {Q} ({\sqrt[{3}]{175}})$ is not monogenic. I don't know how to prove it, though, and I don't know when is $\mathbb {Q} ({\sqrt[{3}]{a}})$ monogenic either. ~2026-29102 (talk) 12:16, 2 January 2026 (UTC)

Well, it appears that even the monogenicity of pure cubic fields is a hard problem. LMFDB lists many cubic fields whose monogenicity is unknown, and there are many pure cubic ones. Samarium-147 (talk) 19:01, 11 January 2026 (UTC)