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Theorems · Theorem · field theory

IsAlgClosure.isAlgClosed

∀ (R : Type u) {K : Type v} {inst : CommRing R} {inst_1 : Field K} {inst_2 : Algebra R K}
  {inst_3 : Module.IsTorsionFree R K} [self : IsAlgClosure R K], IsAlgClosed K
Defined in
Mathlib.FieldTheory.IsAlgClosed.Basic
Cited by
3 results in Mathlib
Foundations
Depth 46 from the axioms · uses propext, Quot.sound
Assumes
IsAlgClosure
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

isSepClosed_iff_isPurelyInseparable_algebraicClosure · cited by 1isSepClosed_iff_isPurelyI…isAlgClosure_iff · cited by 0isAlgClosure_iffIsAlgClosure.ofAlgebraic · cited by 0IsAlgClosure.ofAlgebraicCommRing · cited by 17173CommRingAlgebra · cited by 11388AlgebraField · cited by 7404FieldModule.IsTorsionFree · cited by 600Module.IsTorsionFreeIsAlgClosed · cited by 150IsAlgClosedIsAlgClosure · cited by 16IsAlgClosureIsAlgClosure.isAlgClosedCITED BYCITES

Cites6

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by3

Results whose statement or proof uses this declaration.