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Theorems · Theorem · commutative algebra

FractionalIdeal.canonicalEquiv_coeIdeal

∀ {R : Type u_1} [inst : CommRing R] (S : Submonoid R) (P : Type u_2) [inst_1 : CommRing P] [inst_2 : Algebra R P]
  (P' : Type u_3) [inst_3 : CommRing P'] [inst_4 : Algebra R P'] [inst_5 : IsLocalization S P]
  [inst_6 : IsLocalization S P'] (I : Ideal R), (FractionalIdeal.canonicalEquiv S P P') ↑I = ↑I
Defined in
Mathlib.RingTheory.FractionalIdeal.Operations
Cited by
2 results in Mathlib
Foundations
Depth 90 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingCommRingAlgebraCommRingAlgebraIsLocalizationIsLocalization
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Around this declaration

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

ClassGroup.equiv_mk0 · cited by 1ClassGroup.equiv_mk0FractionalIdeal.canonicalEquiv_mk0 · cited by 1FractionalIdeal.canonical…DFunLike.coe · cited by 62936DFunLike.coeRingHom.id · cited by 18349RingHom.idCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraIdeal · cited by 4748IdealAlgebra.algebraMap · cited by 4706Algebra.algebraMapSubmonoid · cited by 3086SubmonoidRingEquiv · cited by 1147RingEquivIsLocalization · cited by 636IsLocalizationFractionalIdeal · cited by 423FractionalIdealFractionalIdeal.coeIdeal · cited by 109FractionalIdeal.coeIdealIsLocalization.map · cited by 99IsLocalization.mapIsLocalization.map_eq · cited by 34IsLocalization.map_eqFractionalIdeal.canonicalEquiv · cited by 19FractionalIdeal.canonical…FractionalIdeal.ext · cited by 13FractionalIdeal.extFractionalIdeal.canonicalEqui…CITED BYCITES

Cites15

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Cited by2

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