Theorems · Theorem · commutative algebra
mem_integralClosure_iff
∀ (R : Type u_1) (A : Type u_2) [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : Algebra R A] {a : A},
a ∈ integralClosure R A ↔ IsIntegral R a- 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.
Cites5
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
- Subalgebrastatement · cited by 1,353
- IsIntegralstatement · cited by 427
- integralClosurestatement · cited by 105
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.denominator_dvd_iffproof · cited by 3
- NumberField.finite_setOfPred_prod_infinitePlace_iSup_leproof · cited by 2
- isIntegral_of_isIntegralElem_of_monic_of_natDegree_ltproof · cited by 1