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