Theorems · Theorem · commutative algebra
IsAdjoinRoot.ofAlgEquiv_algEquiv
∀ {R : Type u} {S : Type v} [inst : CommRing R] [inst_1 : Ring S] {f : Polynomial R} [inst_2 : Algebra R S]
(h : IsAdjoinRoot S f) {T : Type u_1} [inst_3 : Ring T] [inst_4 : Algebra R T] {U : Type u_2} [inst_5 : Ring U]
[inst_6 : Algebra R U] (h'' : IsAdjoinRoot U f) (e : S ≃ₐ[R] T),
(h.ofAlgEquiv e).algEquiv h'' = e.symm.trans (h.algEquiv h'')- Defined in
- Mathlib.RingTheory.IsAdjoinRoot
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites17
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- Polynomialstatement and proof · cited by 5,681
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.symmstatement and proof · cited by 615
- AlgEquiv.transstatement · cited by 108
- AlgEquiv.apply_symm_applyproof · cited by 67
- IsAdjoinRootstatement and proof · cited by 61
- AlgEquiv.extproof · cited by 60
- IsAdjoinRoot.algEquivstatement · cited by 12
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