EMIS ELibM Electronic Journals Publications de l'Institut Mathématique, Nouvelle Série
Vol. 97(111), pp. 181–186 (2015)

Previous Article

Next Article

Contents of this Issue

Other Issues

ELibM Journals

ELibM Home


Pick a mirror


Centers of Skew Polynomial Rings

Waldo Arriagada and Hugo Ramirez

Department of Applied Mathematics and Sciences, Khalifa University, Al Zafranah, Abu Dhabi, United Arab Emirates ;Instituto de Ciencias Fisicas y Matematicas, Universidad Austral de Chile, Valdivia, Chile

Abstract: We determine the center $\mathcal C(K[x;\delta])$ of the ring of skew polynomials $K[x;\delta]$, where $K$ is a field and $\delta$ is a non-zero derivation over $K$. We prove that $\mathcal C(K[x;\delta])=\ker\delta,$ if $\delta$ is transcendental over $K$. On the contrary, if $\delta$ is algebraic over $K$, then $\mathcal C(K[x;\delta])=(\ker\delta)[\eta(x)]$. The term $\eta(x)$ is the minimal polynomial of $\delta$ over $K$.

Keywords: derivation; skew polynomial; center; ring; commutator

Classification (MSC2000): 12E15; 12E10

Full text of the article: (for faster download, first choose a mirror)

Electronic fulltext finalized on: 16 Apr 2015. This page was last modified: 21 Apr 2015.

© 2015 Mathematical Institute of the Serbian Academy of Science and Arts
© 2015 FIZ Karlsruhe / Zentralblatt MATH for the EMIS Electronic Edition