Papers
Topics
Authors
Recent
Gemini 2.5 Flash
Gemini 2.5 Flash
173 tokens/sec
GPT-4o
7 tokens/sec
Gemini 2.5 Pro Pro
46 tokens/sec
o3 Pro
4 tokens/sec
GPT-4.1 Pro
38 tokens/sec
DeepSeek R1 via Azure Pro
28 tokens/sec
2000 character limit reached

Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings (1305.6035v3)

Published 26 May 2013 in math.RA

Abstract: The first part of the paper will describe a recent result of K. Retert in (\cite{Ret}) for $k[x_1,\ldots,x_n]$ and $k[[x_1,\ldots,x_n]]$. This result states that if $\mathfrak{D}$ is a set of commute $k$-derivations of $k[x,y]$ such that both $\partial_x \in \mathfrak{D}$ and the ring is $\mathfrak{D}$-simple, then there is $d \in \mathfrak{D}$ such that $k[x,y]$ is ${\partial_x,d}$-simple. As applications, we obtain relationships with known results of A. Nowicki on commutative bases of derivations.

Summary

We haven't generated a summary for this paper yet.