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A note on the simplicity of skew polynomial rings of derivation type. (English) Zbl 1117.16016
Summary: In earlier papers we have obtained necessary and sufficient conditions for the simplicity of an iterated skew polynomial ring defined over a ring \(R\) with respect to a finite set of derivations of \(R\) commuting with each other.
In the present paper a sufficient condition is obtained for the simplicity of an iterated skew polynomial ring defined over a ring \(R\) of characteristic zero with respect to a finite set of derivations of \(R\) not necessarily commuting with each other. As an application we construct such a ring over the coordinate ring of the real sphere.

MSC:
16S36 Ordinary and skew polynomial rings and semigroup rings
16W25 Derivations, actions of Lie algebras
16D60 Simple and semisimple modules, primitive rings and ideals in associative algebras
16D30 Infinite-dimensional simple rings (except as in 16Kxx)
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References:
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