Theorems · Theorem · commutative algebra

exists_integral_multiples

∀ (A : Type u_1) (K : Type u_2) [inst : CommRing A] [inst_1 : Field K] [inst_2 : Algebra A K] [IsFractionRing A K]
  {L : Type u_3} [inst_4 : Field L] [inst_5 : Algebra K L] [inst_6 : Algebra A L] [IsScalarTower A K L]
  [FiniteDimensional K L] [IsDomain A] (s : Finset L), ∃ y, y ≠ 0 ∧ ∀ x ∈ s, IsIntegral A (y • x)

Send a set of xs in a finite extension L of the fraction field of R to (y : R) • x ∈ integralClosure R L.

Defined in

Mathlib.RingTheory.DedekindDomain.IntegralClosure

Cited by

1 results in Mathlib

Foundations

Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingFieldAlgebraAlgebraIsScalarTowerFiniteDimensionalIsDomain