Theorems · Theorem · commutative algebra
le_integralClosure_iff_isIntegral
∀ {R : Type u_1} {A : Type u_2} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {S : Subalgebra R A},
S ≤ integralClosure R A ↔ Algebra.IsIntegral R ↥S- Cited by
- 3 results in Mathlib
- Foundations
- Depth 136 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites12
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
- Algebra.algebraMapproof · cited by 4,706
- Subalgebrastatement and proof · cited by 1,353
- IsIntegralproof · cited by 427
- Algebra.IsIntegralstatement · cited by 224
- Subtype.coe_injectiveproof · cited by 205
- integralClosurestatement · cited by 105
- isIntegral_algebraMap_iffproof · cited by 14
- Algebra.isIntegral_defproof · cited by 6
- SetLike.forallproof · cited by 3
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.IsIntegral.adjoinproof · cited by 2
- isIntegral_of_isIntegralElem_of_monic_of_natDegree_ltproof · cited by 1
- integralClosure_eq_top_iffproof · cited by 0