The semiprimeness conjecture for bounded skew power series rings

Let QQ be a simple artinian Zp\mathbb{Z}_p-algebra carrying a standard filtration uu. Let (σ,δ)(\sigma,\delta) be a commuting skew derivation on QQ, meaning that

sigmadelta=deltasigma.sigmadelta=deltasigma.

Assume that (σ,δ)(\sigma,\delta) is quasi-compatible with uu, and let Q+[[x;σ,δ]]Q^+[[x;\sigma,\delta]] denote the bounded skew power series ring.

Semiprimeness conjecture. The ring Q+[[x;σ,δ]]Q^+[[x;\sigma,\delta]] is (semi)prime.

The bounded skew power series ring is known to exist under these hypotheses. If this conjecture holds, the filtered localisation procedure would imply that every skew power series ring over a complete, filtered prime ring is (semi)prime, answering the corresponding question about Iwasawa algebras positively.

Sources & referencesView supporting material

Primary source

Adam Jones and William Woods, “Skew power series rings with automorphisms of finite inner order”, arXiv:2508.21160 (2025).

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