2024/08/20 by Adam Jones, Jones, Adam, William Woods +1
Mathematics · #Advanced Topics in Algebra #Rings, Modules, and Algebras #Algebraic structures and combinatorial models
paper · pdf · doi:10.48550/arxiv.2408.10545
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.