The centralizer of a locally nilpotent R-derivation of the polynomial R-algebra in two variables

IF 0.7 2区数学 Q2 MATHEMATICS

Journal of Pure and Applied Algebra Pub Date : 2024-10-22 DOI:10.1016/j.jpaa.2024.107828

M'hammed El Kahoui, Najoua Essamaoui, Mustapha Ouali

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引用次数: 0

Abstract

Let R be an integral domain containing

Q

and ξ be an irreducible nontrivial locally nilpotent R-derivation of the polynomial R-algebra A in two variables. In this paper we investigate the group

{Aut}_{R} (A, ξ)

of R-automorphisms of A which commute with ξ. In the case R is a unique factorization domain and the plinth ideal of ξ is principal we give a complete description of the subgroup

{SAut}_{R} (A, ξ)

{Aut}_{R} (A, ξ)

consisting of Jacobian one automorphisms. If moreover R contains a field K such that the group of units of R is

K^{⋆}

we prove that

{Aut}_{R} (A, ξ) = {SAut}_{R} (A, ξ)

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二变量多项式 R 代数的局部零势 R 派生的中心子

设 R 是包含 Q 的积分域，ξ 是两变量多项式 R 代数 A 的不可还原的非琐局部无穷 R 衍射。在本文中，我们将研究与ξ换元的 A 的 R 自变量群 AutR(A,ξ)。在 R 是唯一因式分解域且 ξ 的柱顶理想是主理想的情况下，我们给出了 AutR(A,ξ) 的子群 SAutR(A,ξ) 的完整描述，该子群由雅各布一自形化组成。如果 R 还包含一个域 K，使得 R 的单位群是 K⋆，我们就可以证明 AutR(A,ξ)=SAutR(A,ξ)。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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来源期刊

Journal of Pure and Applied Algebra 数学-数学

CiteScore

1.70

自引率

12.50%

发文量

225

审稿时长

17 days

期刊介绍： The Journal of Pure and Applied Algebra concentrates on that part of algebra likely to be of general mathematical interest: algebraic results with immediate applications, and the development of algebraic theories of sufficiently general relevance to allow for future applications.