Theorems · Theorem · field theory
IsAlgClosure.of_splits
∀ {R : Type u_1} {K : Type u_2} [inst : CommRing R] [IsDomain R] [inst_2 : Field K] [inst_3 : Algebra R K]
[Algebra.IsIntegral R K] [inst_5 : Module.IsTorsionFree R K],
(∀ (p : Polynomial R), p.Monic → Irreducible p → (Polynomial.map (algebraMap R K) p).Splits) → IsAlgClosure R K- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 141 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites22
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- LT.lt.ne'proof · cited by 1,417
- Polynomial.mapstatement and proof · cited by 806
- Polynomial.evalproof · cited by 796
- Module.IsTorsionFreestatement and proof · cited by 600
- Irreduciblestatement and proof · cited by 496
- Polynomial.Monicstatement and proof · cited by 461
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosure.of_exists_rootproof · cited by 1