Theorems · Theorem · commutative algebra

FractionalIdeal.one_le_extendedHom_iff

∀ {A : Type u_1} {K : Type u_2} (L : Type u_3) (B : Type u_4) [inst : CommRing A] [inst_1 : IsDomain A]
  [inst_2 : CommRing B] [inst_3 : IsDomain B] [inst_4 : Algebra A B] [inst_5 : Module.IsTorsionFree A B]
  [inst_6 : Field K] [inst_7 : Field L] [inst_8 : Algebra A K] [inst_9 : Algebra B L] [inst_10 : IsFractionRing A K]
  [inst_11 : IsFractionRing B L] {I : FractionalIdeal (nonZeroDivisors A) K} [inst_12 : Algebra K L]
  [inst_13 : Algebra A L] [IsScalarTower A B L] [IsScalarTower A K L] [Algebra.IsIntegral A B] [IsDedekindDomain A]
  [IsDedekindDomain B], I ≠ 0 → (1 ≤ (FractionalIdeal.extendedHom L B) I ↔ 1 ≤ I)

Defined in

Mathlib.RingTheory.FractionalIdeal.Extended

Cited by

2 results in Mathlib

Foundations

Depth 145 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainCommRingIsDomainAlgebraModule.IsTorsionFreeFieldFieldAlgebraAlgebraIsFractionRingIsFractionRingAlgebraAlgebraIsScalarTowerIsScalarTowerAlgebra.IsIntegralIsDedekindDomainIsDedekindDomain