Theorems · Theorem · commutative algebra

map_equiv_traceDual

∀ (A : Type u_1) (K : Type u_2) {L : Type u} {B : Type u_3} [inst : CommRing A] [inst_1 : Field K] [inst_2 : CommRing B]
  [inst_3 : Field L] [inst_4 : Algebra A K] [inst_5 : Algebra B L] [inst_6 : Algebra A B] [inst_7 : Algebra K L]
  [inst_8 : Algebra A L] [inst_9 : IsScalarTower A K L] [inst_10 : IsScalarTower A B L] [IsFractionRing A K]
  [inst_12 : IsDomain A] [inst_13 : IsFractionRing B L] [inst_14 : IsDomain B] [inst_15 : FaithfulSMul A B]
  (I : Submodule B (FractionRing B)),
  Submodule.map (FractionRing.algEquiv B L).toLinearMap (Submodule.traceDual A (FractionRing A) I) =
    Submodule.traceDual A K (Submodule.map (FractionRing.algEquiv B L).toLinearMap I)

Defined in

Mathlib.RingTheory.DedekindDomain.Different

Cited by

1 results in Mathlib

Foundations

Depth 110 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldCommRingFieldAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsFractionRingIsDomainIsFractionRingIsDomainFaithfulSMul