Theorems · Theorem · field theory
IsAlgClosure.of_exists_root
∀ {F : Type u_1} {E : Type u_2} [inst : Field F] [inst_1 : Field E] [inst_2 : Algebra F E]
[alg : Algebra.IsAlgebraic F E],
(∀ (p : Polynomial F), p.Monic → Irreducible p → ∃ x, (Polynomial.aeval x) p = 0) → IsAlgClosure F E- Defined in
- Mathlib.FieldTheory.Isaacs
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 155 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites23
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement and proof · cited by 62,936
- Algebrastatement and proof · cited by 11,388
- Fieldstatement and proof · cited by 7,404
- Polynomialstatement and proof · cited by 5,681
- Algebra.algebraMapproof · cited by 4,706
- AlgHomstatement and proof · cited by 3,236
- Polynomial.mapproof · cited by 806
- Polynomial.aevalstatement and proof · cited by 615
- Irreduciblestatement and proof · cited by 496
- Polynomial.Monicstatement and proof · cited by 461
- minpolyproof · cited by 439
- IsIntegralproof · cited by 427
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosure.of_exist_rootsproof · cited by 0