Theorems · Theorem · field theory
IsAlgClosed.algebraMap_bijective_of_isIntegral
∀ {k : Type u_1} {K : Type u_2} [inst : Field k] [inst_1 : Ring K] [IsDomain K] [hk : IsAlgClosed k]
[inst_3 : Algebra k K] [Algebra.IsIntegral k K], Function.Bijective ⇑(algebraMap k K)- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 116 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites32
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
- RingHomstatement · cited by 10,189
- Ringstatement and proof · cited by 7,463
- Fieldstatement and proof · cited by 7,404
- Polynomialproof · cited by 5,681
- Algebra.algebraMapstatement and proof · cited by 4,706
- one_mulproof · cited by 2,841
- IsDomainstatement and proof · cited by 2,196
- Polynomial.Xproof · cited by 1,639
- Polynomial.Cproof · cited by 1,598
- Polynomial.coeffproof · cited by 1,045
Cited by6
Results whose statement or proof uses this declaration.
- IsSimpleModule.algebraMap_end_bijective_of_isAlgClosedproof · cited by 2
- Algebra.FormallyUnramified.bijective_of_isAlgClosed_of_isLocalRingproof · cited by 1
- IntermediateField.eq_bot_of_isAlgClosed_of_isAlgebraicproof · cited by 1
- IsSimpleRing.exists_algEquiv_matrix_of_isAlgClosedproof · cited by 0
- IsAlgClosed.ringHom_bijective_of_isIntegralproof · cited by 0
- IsSemisimpleRing.exists_algEquiv_pi_matrix_of_isAlgClosedproof · cited by 0