Theorems · Theorem · commutative algebra
isIntegral_algEquiv
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_5} {B : Type u_6} [inst_1 : Ring A] [inst_2 : Ring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A ≃ₐ[R] B) {x : A}, IsIntegral R (f x) ↔ IsIntegral R x- Cited by
- 3 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Ringstatement and proof · cited by 7,463
- AlgEquivstatement and proof · cited by 1,681
- AlgEquiv.symmproof · cited by 615
- IsIntegralstatement and proof · cited by 427
- AlgEquiv.symm_apply_applyproof · cited by 36
- IsIntegral.mapproof · cited by 22
Cited by3
Results whose statement or proof uses this declaration.
- IsIntegrallyClosed.of_equivproof · cited by 3
- IsIntegralClosure.of_algEquivproof · cited by 1
- AlgEquiv.isPurelyInseparableproof · cited by 1