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Simplicity of partial and Schmidt differential operator rings. (English) Zbl 0608.16005
We develop necessary and sufficient conditions for certain differential operator rings to be simple. We do this for a ring with finitely many commuting derivations and for a ring with a commuting Schmidt higher derivation of finite length. Also we give a correspondence between finite sets of derivations and Schmidt higher derivations.

MSC:
16W60 Valuations, completions, formal power series and related constructions (associative rings and algebras)
16W20 Automorphisms and endomorphisms
16D30 Infinite-dimensional simple rings (except as in 16Kxx)
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