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Theorems · Definition · number theory

IsNonarchimedeanLocalField.valueGroupWithZeroIsoInt

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : ValuativeRel K] →
      [inst_2 : TopologicalSpace K] →
        [IsNonarchimedeanLocalField K] → ValuativeRel.ValueGroupWithZero K ≃*o WithZero (Multiplicative ℤ)

The value group of a local field is (uniquely) isomorphic to ℤᵐ⁰.

Defined in
Mathlib.NumberTheory.LocalField.Basic
Cited by
0 results in Mathlib
Foundations
Depth 103 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldValuativeRelTopologicalSpaceIsNonarchimedeanLocalField
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TopologicalSpace · cited by 24529TopologicalSpaceField · cited by 7404FieldMultiplicative · cited by 875MultiplicativeWithZero · cited by 586WithZeroNonempty.some · cited by 340Nonempty.someValuativeRel · cited by 241ValuativeRelOrderMonoidIso · cited by 114OrderMonoidIsoValuativeRel.ValueGroupWithZero · cited by 86ValuativeRel.ValueGroupWi…IsNonarchimedeanLocalField · cited by 1IsNonarchimedeanLocalFieldIsNonarchimedeanLocalField.va…CITED BYCITES

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