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

Centers of Skew Polynomial RingsWaldo Arriagada and Hugo RamirezDepartment 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, ChileAbstract: 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 nonzero 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.
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