Geodesic
Simple Skew Polynomial Rings
Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 37
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We treat two questions. First we give the general conditions for the existence of skew polynomial rings in finitely many variables over a given ring $R$ (special cases of such rings are well, known, typifield by the $n$-th Weyl Algebras) and second we obtain the necesary and sufficient conditions for the simplicity of such rings. Note that Amitsur [1] obtained conditions under which an Ore extension $R[x,d]$ over a simple ring $R$ is simple, while more recently Jordan [6] obtained such conditions if $R$ is $d$-simple.
Classification : 16A05 
@article{PIM_1985_N_S_37_51_a7,
     author = {Michael G. Voskoglou},
     title = {Simple {Skew} {Polynomial} {Rings}},
     journal = {Publications de l'Institut Math\'ematique},
     pages = {37 },
     year = {1985},
     volume = {_N_S_37},
     number = {51},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a7/}
}
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Michael G. Voskoglou. Simple Skew Polynomial Rings. Publications de l'Institut Mathématique, _N_S_37 (1985) no. 51, p. 37 . http://geodesic.mathdoc.fr/item/PIM_1985_N_S_37_51_a7/