Theorems · Theorem · commutative algebra

Submodule.one_le_traceDual_one

∀ {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]
  [IsIntegrallyClosed A] [FiniteDimensional K L] [IsIntegralClosure B A L], 1 ≤ Submodule.traceDual A K 1

Defined in

Mathlib.RingTheory.DedekindDomain.Different

Cited by

0 results in Mathlib

Foundations

Depth 181 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldCommRingFieldAlgebraAlgebraAlgebraAlgebraAlgebraIsScalarTowerIsScalarTowerIsFractionRingIsIntegrallyClosedFiniteDimensionalIsIntegralClosure