Simplicity and Commutative Bases of Derivations in Polynomial and Power Series Rings. (12th December 2013)

• Record Type: Journal Article
• Authors: Baltazar, Rene
• Other Names: Chen H. Academic Editor.; Zimmermann A. Academic Editor.
• Is Part Of: ISRN algebra. Volume 2013(2013)
• Publication Date: 2013-12-12
• Subjects: Algebra -- Periodicals; Algebra; Periodicals; Electronic journals; 512
• DOI: 10.1155/2013/560648
• Languages: English
• ISSNs: 2090-6285

Abstract

Abstract : The first part of the paper will describe a recent result of Retert in (2006) for k x 1, …, x n and k x 1, …, x n . This result states that if 𝔇 is a set of commute k -derivations of k x, y such that both ∂ x ∈ 𝔇 and the ring is 𝔇 -simple, then there is d ∈ 𝔇 such that k x, y is ∂ x, d -simple. As for applications, we obtain relationships with known results of A. Nowicki on commutative bases of derivations.