Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings

2013/05/26 by Rene Baltazar, Baltazar, Rene
Engineering · Mathematics · Physics and Astronomy · #Advanced Differential Equations and Dynamical Systems #Advanced Differential Geometry Research #Advanced Topics in Algebra #Control and Dynamics of Mobile Robots #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA

paper · pdf · doi:10.48550/arxiv.1305.6035

openalex publication_date 2013/05/26 · arxiv created 2013/12/02 · arxiv updated 2013/12/03 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

The first part of the paper will describe a recent result of K. Retert in (\citeRet) for k[x₁,…,x_n] and k[[x₁,…,x_n]]. This result states that if \mathfrakD is a set of commute k-derivations of k[x,y] such that both ∂_x ∈ \mathfrakD and the ring is \mathfrakD-simple, then there is d ∈ \mathfrakD such that k[x,y] is \∂_x,d\-simple. As applications, we obtain relationships with known results of A. Nowicki on commutative bases of derivations.

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