Theorems · Definition · number theory

NumberField.mixedEmbedding.fundamentalCone.idealSetMap

(K : Type u_1) →
  [inst : Field K] →
    [inst_1 : NumberField K] →
      (J : ↥(nonZeroDivisors (Ideal (NumberField.RingOfIntegers K)))) →
        ↑(NumberField.mixedEmbedding.fundamentalCone.idealSet K J) →
          ↑(NumberField.mixedEmbedding.fundamentalCone.integerSet K)

The map that sends a : idealSet to an element of integerSet. This map exists because J is an integral ideal.

Defined in: Mathlib.NumberTheory.NumberField.CanonicalEmbedding.FundamentalCone
Cited by: 2 results in Mathlib
Foundations: Depth 329 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Field NumberField

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Cites10

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

Fieldstatement and proof · cited by 7,404
Set.Elemstatement and proof · cited by 7,166
Idealstatement and proof · cited by 4,748
Submonoidstatement · cited by 3,086
nonZeroDivisorsstatement and proof · cited by 895
NumberFieldstatement and proof · cited by 653
NumberField.RingOfIntegersstatement and proof · cited by 413
NumberField.mixedEmbedding.mixedSpacestatement and proof · cited by 239
NumberField.mixedEmbedding.fundamentalCone.integerSetstatement and proof · cited by 22
NumberField.mixedEmbedding.fundamentalCone.idealSetstatement and proof · cited by 8

Cited by3

Results whose statement or proof uses this declaration.

NumberField.mixedEmbedding.fundamentalCone.idealSetEquivproof · cited by 4
NumberField.mixedEmbedding.fundamentalCone.idealSetMap_applystatement · cited by 0
NumberField.mixedEmbedding.fundamentalCone.preimage_of_IdealSetMapstatement · cited by 0