Bounded skew power series rings for inner $σ$-derivations

Résumé fourni par la source

We define and explore the bounded skew power series ring $R^+[[x;σ,δ]]$ defined over a complete, filtered, Noetherian prime ring $R$ with a commuting skew derivation $(σ,δ)$. We establish precise criteria for when this ring is well-defined, and for an appropriate completion $Q$ of $Q(R)$, we prove that if $Q$ has characteristic $p$, $δ$ is an inner $σ$-derivation and no positive power of $σ$ is inner as an automorphism of $Q$, then $Q^+[[x;σ,δ]]$ is often prime, and even simple under certain mild restrictions on $δ$. It follows from this result that $R^+[[x;σ,δ]]$ is itself prime.

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