Geodesic
Centers of Skew Polynomial Rings
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 181

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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 $K$.
DOI : 10.2298/PIM131217001A
Classification : 12E15, 12E10
Keywords: derivation, skew polynomial, center, ring, commutator 
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Waldo Arriagada; Hugo Ramírez. Centers of Skew Polynomial Rings. Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 181 . doi: 10.2298/PIM131217001A

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