Defectless polynomials over henselian fields and inductive valuations

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Let (K,v) be a henselian valued field. Let Pdless⊂K[x] be the set of monic, irreducible polynomials which are defectless and have degree greater than one. For a certain equivalence relation ≈ on Pdless, we establish a canonical bijection M→Pdless/≈, where M is a discrete MacLane space, constructed in terms of inductive valuations on K[x] extending v.




Moraes de Oliveira, N., & Nart, E. (2020). Defectless polynomials over henselian fields and inductive valuations. Journal of Algebra, 541, 270–307.

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