Theorems · Definition · number theory

NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      Quotient
          (MulAction.orbitRel ↥(NumberField.Units.torsion K)
            ↑(NumberField.mixedEmbedding.fundamentalCone.integerSet K)) ≃
        Associates ↥(nonZeroDivisors (NumberField.RingOfIntegers K))

The equivalence between integerSet K modulo torsion K and Associates (𝓞 K)⁰.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 1 results in Mathlib
Foundations: Depth 337 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites16

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Equivstatement · cited by 8,337
Fieldstatement and proof · cited by 7,404
Set.Elemstatement · cited by 7,166
Subgroupstatement · cited by 3,593
Submonoidstatement · cited by 3,086
Unitsstatement · cited by 2,804
nonZeroDivisorsstatement · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement · cited by 413
NumberField.mixedEmbedding.mixedSpacestatement · cited by 239
Associatesstatement · cited by 210
MulAction.orbitRelstatement · cited by 114

Cited by2

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.integerSetEquivproof · cited by 2
NumberField.mixedEmbedding.fundamentalCone.integerSetQuotEquivAssociates_applystatement · cited by 0