Let G ⊂ xFq [x] (q is a power of the prime p) be a subset of formal power series over a finite field such that it forms a compact abelian p-adic Lie group of dimension d ≥ 1. We establish a necessary and sufficient condition for the APF extension of local field corresponding to (Fq(x), G) under the field of norms functor to be an extension of p-adic fields. We then apply this result to study invertible power series over a ring of p-adic integers which commute with a fixed noninvertible power series under composition.
ASJC Scopus subject areas
- Algebra and Number Theory