Table of Contents
ISRN Algebra
Volume 2013 (2013), Article ID 560648, 4 pages
http://dx.doi.org/10.1155/2013/560648
Research Article

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

Universidade Federal do Rio Grande do Sul (UFRGS), Campus do Vale, Código Postal 15051, 91501-970 Porto Alegre, RS, Brazil

Received 8 October 2013; Accepted 24 November 2013

Academic Editors: H. Chen and A. Zimmermann

Copyright © 2013 Rene Baltazar. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

The first part of the paper will describe a recent result of Retert in (2006) for and . This result states that if is a set of commute -derivations of such that both and the ring is -simple, then there is such that is -simple. As for applications, we obtain relationships with known results of A. Nowicki on commutative bases of derivations.