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Theorems · Theorem · number theory

NumberField.Units.coe_ne_zero

∀ {K : Type u_1} [inst : Field K] (x : (NumberField.RingOfIntegers K)ˣ),
  (algebraMap (NumberField.RingOfIntegers K) K) ↑x ≠ 0
Defined in
Mathlib.NumberTheory.NumberField.Units.Basic
Cited by
5 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
Field
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Around this declaration

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

NumberField.Units.pos_at_place · cited by 2Units.pos_at_placeNumberField.mixedEmbedding.fundamentalCone.sum_eq_zero_of_mem_span_completeFamily · cited by 1fundamentalCone.sum_eq_ze…NumberField.Units.abs_det_eq_abs_det · cited by 1Units.abs_det_eq_abs_detNumberField.mixedEmbedding.fundamentalCone.realSpaceToLogSpace_completeFamily_of_ne · cited by 1fundamentalCone.realSpace…NumberField.Units.dirichletUnitTheorem.unitLattice_inter_ball_finite · cited by 0dirichletUnitTheorem.unit…DFunLike.coe · cited by 62936DFunLike.coeRingHom · cited by 10189RingHomField · cited by 7404FieldAlgebra.algebraMap · cited by 4706Algebra.algebraMapUnits · cited by 2804UnitsUnits.val · cited by 1966Units.valNumberField.RingOfIntegers · cited by 413NumberField.RingOfIntegersSubtype.coe_injective · cited by 205Subtype.coe_injectiveUnits.ne_zero · cited by 68Units.ne_zeroUnits.coe_ne_zeroCITED BYCITES

Cites9

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Cited by5

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