Noncommutative symmetric functions and Wpolynomials
Abstract
Let K,S,D be a division ring, an endomorphism and a Sderivation of K, respectively. In this setting we introduce generalized noncommutative symmetric functions and obtain Vieta formula and decompositions of differential operators. Wpolynomials show up naturally, their connections with Pindependency, Vandermonde and Wronskian matrices are briefly studied. The different linear factorizations of Wpolynomials are analysed. Connections between the existence of LLCM of monic linear polynomials with coefficients in a ring and the left duo property are established at the end of the paper.
 Publication:

arXiv Mathematics eprints
 Pub Date:
 June 2006
 arXiv:
 arXiv:math/0606614
 Bibcode:
 2006math......6614D
 Keywords:

 Mathematics  Rings and Algebras;
 16S36