Theorems · Theorem · field theory
IsAlgClosure.equivOfEquiv_symm_comp_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),
(↑(IsAlgClosure.equivOfEquiv L M hSR).symm).comp (algebraMap R M) = (algebraMap S L).comp ↑hSR.symm- Defined in
- Mathlib.FieldTheory.IsAlgClosed.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 158 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites15
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
- 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
- RingHom.compstatement · cited by 899
- RingHomClass.toRingHomstatement · cited by 746
- Module.IsTorsionFreestatement and proof · cited by 600
- RingEquiv.symmstatement · cited by 567
- RingHom.ext_iffproof · cited by 16
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