Simple skew polynomial rings

Michael G. Voskoglou

Abstract: 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. \par 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 (MSC2000): 16A05

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