Geodesic
Centers of Skew Polynomial Rings
Publications de l'Institut Mathématique, _N_S_97 (2015) no. 111, p. 181 Cet article a éte moissonné depuis la source eLibrary of Mathematical Institute of the Serbian Academy of Sciences and Arts

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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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     author = {Waldo Arriagada and Hugo Ram{\'\i}rez},
     title = {Centers of {Skew} {Polynomial} {Rings}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {181 },
     year = {2015},
     volume = {_N_S_97},
     number = {111},
     doi = {10.2298/PIM131217001A},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.2298/PIM131217001A/}
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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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