Theorems · Theorem · field theory
IsAlgClosure.equivOfEquiv_algebraMap
∀ {R : Type u} {S : Type u_3} (L : Type v) (M : Type w) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Field L]
[inst_3 : Field M] [inst_4 : Algebra R M] [inst_5 : Module.IsTorsionFree R M] [inst_6 : IsAlgClosure R M]
[inst_7 : Algebra S L] [inst_8 : Module.IsTorsionFree S L] [inst_9 : IsAlgClosure S L] [inst_10 : IsDomain R]
[inst_11 : IsDomain S] (hSR : S ≃+* R) (s : S),
(IsAlgClosure.equivOfEquiv L M hSR) ((algebraMap S L) s) = (algebraMap R M) (hSR s)- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 156 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites13
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- RingHomstatement · cited by 10,189
- Fieldstatement and proof · cited by 7,404
- Algebra.algebraMapstatement · cited by 4,706
- IsDomainstatement and proof · cited by 2,196
- RingEquivstatement and proof · cited by 1,147
- Module.IsTorsionFreestatement and proof · cited by 600
- RingHom.ext_iffproof · cited by 16
- IsAlgClosurestatement and proof · cited by 16
- IsAlgClosure.equivOfEquivstatement · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- IsAlgClosure.equivOfEquiv_symm_algebraMapproof · cited by 1