Residual coordinates over one-dimensional rings

Residual coordinates over one-dimensional rings

Given a noetherian ring R and n≥2, it is well-known that residual coordinates of the polynomial algebra R[n] are m-stable coordinates for some m≥1, that is they become coordinates in the larger polynomial algebra R[n+m]. In this paper we prove that, over a large class of noetherian one-dimensional r...

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Veröffentlicht in:Journal of pure and applied algebra 2021-06, Vol.225 (6), p.106629, Article 106629
Hauptverfasser: El Kahoui, M'hammed, Essamaoui, Najoua, Ouali, Mustapha
Format: Artikel
Sprache:eng
Schlagworte:
Local coordinate
Polynomial automorphism
Residual coordinate
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Zusammenfassung:Given a noetherian ring R and n≥2, it is well-known that residual coordinates of the polynomial algebra R[n] are m-stable coordinates for some m≥1, that is they become coordinates in the larger polynomial algebra R[n+m]. In this paper we prove that, over a large class of noetherian one-dimensional rings, m=1 is enough. This includes affine algebras over an algebraically closed field as well as noetherian complete local rings containing a field.
ISSN:0022-4049
1873-1376
DOI:10.1016/j.jpaa.2020.106629