Theorems · Theorem · field theory
RatFunc.coe_mapAlgHom_eq_coe_map
∀ {K : Type u} [inst : CommRing K] [inst_1 : IsDomain K] {R : Type u_2} {S : Type u_3} [inst_2 : CommRing R]
[inst_3 : IsDomain R] [inst_4 : CommSemiring S] [inst_5 : Algebra S (Polynomial K)]
[inst_6 : Algebra S (Polynomial R)] (φ : Polynomial K →ₐ[S] Polynomial R)
(hφ : nonZeroDivisors (Polynomial K) ≤ Submonoid.comap φ (nonZeroDivisors (Polynomial R))),
⇑(RatFunc.mapAlgHom φ hφ) = ⇑(RatFunc.map φ hφ)- Defined in
- Mathlib.FieldTheory.RatFunc.Basic
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 121 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
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Cites14
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
- CommSemiringstatement and proof · cited by 10,911
- Polynomialstatement and proof · cited by 5,681
- MonoidHomstatement · cited by 3,629
- AlgHomstatement and proof · cited by 3,236
- Submonoidstatement · cited by 3,086
- IsDomainstatement and proof · cited by 2,196
- nonZeroDivisorsstatement and proof · cited by 895
- RatFuncstatement · cited by 301
- Submonoid.comapstatement and proof · cited by 179
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