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Theorems · Theorem · commutative algebra

FractionalIdeal.count.congr_simp

∀ {R : Type u_1} [inst : CommRing R] (K : Type u_2) [inst_1 : Field K] [inst_2 : Algebra R K]
  [inst_3 : IsFractionRing R K] [inst_4 : IsDedekindDomain R] (v v_1 : IsDedekindDomain.HeightOneSpectrum R),
  v = v_1 →
    ∀ (I I_1 : FractionalIdeal (nonZeroDivisors R) K),
      I = I_1 → FractionalIdeal.count K v I = FractionalIdeal.count K v_1 I_1
Defined in
Mathlib.RingTheory.DedekindDomain.Factorization
Cited by
2 results in Mathlib
Foundations
Depth 149 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingFieldAlgebraIsFractionRingIsDedekindDomain
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Around this declaration

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

FractionalIdeal.count_coe_nonneg · cited by 1FractionalIdeal.count_coe…FractionalIdeal.finite_factors · cited by 0FractionalIdeal.finite_fa…CommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraField · cited by 7404FieldnonZeroDivisors · cited by 895nonZeroDivisorsIsFractionRing · cited by 738IsFractionRingIsDedekindDomain · cited by 668IsDedekindDomainFractionalIdeal · cited by 423FractionalIdealIsDedekindDomain.HeightOneSpectrum · cited by 338IsDedekindDomain.HeightOn…FractionalIdeal.count · cited by 25FractionalIdeal.countcount.congr_simpCITED BYCITES

Cites9

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Cited by2

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