Theorems · Theorem · commutative algebra
Subring.integralClosure_le_iff
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_2} [inst_1 : CommRing A] [inst_2 : Algebra R A] {T : Subring A}
[IsIntegrallyClosedIn (↥T) A], (integralClosure R A).toSubring ≤ T ↔ ∀ (r : R), (algebraMap R A) r ∈ T- Cited by
- 1 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.
Cites16
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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · cited by 4,706
- IsScalarTowerproof · cited by 3,896
- Subringstatement and proof · cited by 602
- RingHom.toAlgebraproof · cited by 337
- integralClosurestatement and proof · cited by 105
- IsScalarTower.of_algebraMap_eqproof · cited by 40
- IsIntegral.tower_topproof · cited by 30
- Subalgebra.toSubringstatement and proof · cited by 30
Cited by1
Results whose statement or proof uses this declaration.
- Subring.integralClosure_subring_le_iffproof · cited by 1