On residual and stable coordinates

JOURNAL OF PURE AND APPLIED ALGEBRA

卷:225

Article

Dutta, Amartya Kumar¹  Lahiri, Animesh² 

[1] Indian Stat Inst, Stat & Math Unit, 203 BT Rd, Kolkata 700108, India

[2] Harish Chandra Res Inst, Chhatnag Rd, Prayagraj 211019, Allahabad, India

关键词: Polynomial algebra;    Residual coordinate;    Stable coordinate;    Exponential map;   

DOI  :  10.1016/j.jpaa.2021.106707

来源: Elsevier

【 摘 要 】

In a recent paper [10], M.E. Kahoui and M. Ouali have proved that over an algebraically closed field k of characteristic zero, residual coordinates in k[X] [Z(1), ..., Z(n)] are one-stable coordinates. In this paper we extend their result to the case of an algebraically closed field k of arbitrary characteristic. In fact, we show that the result holds when k[X] is replaced by any one-dimensional seminormal domain R which is affine over an algebraically closed field k. For our proof, we extend a result of S. Maubach in [11] giving a criterion for a polynomial of the form a(X)W + P(X, Z(1), ..., Z(n)) to be a coordinate in k[X] [Z(1), ..., Z(n), W]. Kahoui and Ouali had also shown that over a Noetherian d-dimensional ring R containing Q any residual coordinate in R[Z(1), ..., Z(n)] is an r-stable coordinate, where r = (2(d) - 1)n. We will give a sharper bound for r when R is affine over an algebraically closed field of characteristic zero. (C) 2021 Elsevier B.V. All rights reserved.

【 授权许可】

Free