Theorems · Theorem · commutative algebra

FiniteDimensional.exists_is_basis_integral

∀ (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 b, ∀ (x : ↥s), IsIntegral A (b x)

If L is a finite extension of K = Frac(A), then L has a basis over A consisting of integral elements.

Defined in

Mathlib.RingTheory.DedekindDomain.IntegralClosure

Cited by

1 results in Mathlib

Foundations

Depth 142 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingFieldAlgebraIsFractionRingFieldAlgebraAlgebraIsScalarTowerFiniteDimensionalIsDomain