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Theorems · Theorem · number theory

NumberField.fractionalIdeal_rank

∀ (K : Type u_1) [inst : Field K] [inst_1 : NumberField K]
  (I : (FractionalIdeal (nonZeroDivisors (NumberField.RingOfIntegers K)) K)ˣ),
  Module.finrank ℤ ↥↑↑I = Module.finrank ℤ (NumberField.RingOfIntegers K)
Defined in
Mathlib.NumberTheory.NumberField.FractionalIdeal
Cited by
1 results in Mathlib
Foundations
Depth 190 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
FieldNumberField
Mathlib docsSourceLoogleLeanSearch

Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

NumberField.mixedEmbedding.volume_fundamentalDomain_fractionalIdealLatticeBasis · cited by 3mixedEmbedding.volume_fun…Field · cited by 7404FieldSubmodule · cited by 7192SubmoduleUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valModule.finrank · cited by 1770Module.finrankFintype.card · cited by 1386Fintype.cardnonZeroDivisors · cited by 895nonZeroDivisorsNumberField · cited by 653NumberFieldFractionalIdeal · cited by 423FractionalIdealNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersModule.Free.ChooseBasisIndex · cited by 133Free.ChooseBasisIndexFractionalIdeal.coeToSubmodule · cited by 130FractionalIdeal.coeToSubm…Module.finrank_eq_card_basis · cited by 40Module.finrank_eq_card_ba…Module.finrank_eq_card_chooseBasisIndex · cited by 21Module.finrank_eq_card_ch…NumberField.basisOfFractionalIdeal · cited by 8NumberField.basisOfFracti…NumberField.fractionalIdeal_r…CITED BYCITES

Cites16

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Cited by1

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