Theorems · Theorem · field theory

AlgebraicIndependent.matroid_isFlat_iff

∀ {R : Type u_1} {A : Type w} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A]
  [inst_3 : FaithfulSMul R A] [inst_4 : IsDomain A] {s : Set A},
  (AlgebraicIndependent.matroid R A).IsFlat s ↔ ∃ S, ↑S = s ∧ ∀ (a : A), IsAlgebraic (↥S) a → a ∈ s

Defined in

Mathlib.RingTheory.AlgebraicIndependent.TranscendenceBasis

Cited by

0 results in Mathlib

Foundations

Depth 150 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingCommRingAlgebraFaithfulSMulIsDomain