Theorems · Theorem · commutative algebra
AlgEquiv.isIntegral_iff
∀ {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] (e : A ≃ₐ[R] B), Algebra.IsIntegral R A ↔ Algebra.IsIntegral R B- Cited by
- 3 results in Mathlib
- Foundations
- Depth 115 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.
- 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
- AlgEquiv.toAlgHomproof · cited by 273
- Algebra.IsIntegralstatement and proof · cited by 224
- AlgEquiv.injectiveproof · cited by 61
- Algebra.IsIntegral.of_injectiveproof · cited by 1
Cited by3
Results whose statement or proof uses this declaration.
- IsCyclotomicExtension.integralproof · cited by 2
- Algebra.IsPushout.isIntegral'proof · cited by 1
- integralClosure_eq_top_iffproof · cited by 0