5

Is there a Noether normalisation lemma for finitely generated (flat) algebras over $\mathbf{Z}$ (or more generally principal ideal domains)? It seems one can tensorise with the quotient field and then apply the usual Noether normalisation lemma. I couldn't find this in the literature, so I suspect it is wrong.

  • Related? https://mathoverflow.net/questions/42276/noethers-normalization-lemma-over-a-ring-a – Asvin Oct 20 '17 at 17:14
  • 1
    Isn't this the same question? https://math.stackexchange.com/questions/213336/noether-normalization-over-mathbbz – Asvin Oct 20 '17 at 17:16
  • @Asvin: Thanks! Can one omit the localisation in the case of a PID and a flat algebra? –  Oct 20 '17 at 17:33
  • I haven't actually gone through the links myself. I just remembered seeing similar questions before. Maybe you will find the formulation here more useful? https://mathoverflow.net/a/60716/58001 – Asvin Oct 20 '17 at 17:47
  • @TimoKeller No, just look at the counterexample from the second question, with $\mathbb Z[1/2]$. – Will Sawin Oct 20 '17 at 19:17
  • 1
    Another reference in the literature is Proposition 2.1 of Jouanolou, "Théorèmes de Bertini et applications." – Aaron Landesman Oct 21 '17 at 05:40

1 Answers1

1

you can consult the paper Corrigendum to “Noether Normalization theorem and dynamical Gröbner bases over Bezout domains of Krull dimension 1” [J. Algebra 492 (15) (2017) 52-56] by Maroua Gamanda and Ihsen Yengui.

The link is https://www.sciencedirect.com/science/article/pii/S002186931930314X

user15425
  • 31