Theorems · Theorem · commutative algebra
Algebra.IsIntegral.isIntegral
∀ {R : Type u_1} {A : Type u_3} {inst : CommRing R} {inst_1 : Ring A} {inst_2 : Algebra R A}
[self : Algebra.IsIntegral R A] (x : A), IsIntegral R x- Cited by
- 86 results in Mathlib
- Foundations
- Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Algebra.IsIntegral
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
- Ringstatement and proof · cited by 7,463
- IsIntegralstatement · cited by 427
- Algebra.IsIntegralstatement and proof · cited by 224
Cited by86
Results whose statement or proof uses this declaration.
- IsIntegral.of_finiteproof · cited by 16
- isIntegral_transproof · cited by 15
- IsIntegralClosure.isLocalizationproof · cited by 13
- Ideal.eq_bot_of_comap_eq_botproof · cited by 9
- RingHom.IsIntegral.transproof · cited by 9
- isAlgebraic_of_isFractionRingproof · cited by 6
- IsAlgClosed.algebraMap_bijective_of_isIntegralproof · cited by 6
- Normal.isIntegralproof · cited by 6
- Algebra.IsIntegral.finiteproof · cited by 5
- Ideal.isMaximal_of_isIntegral_of_isMaximal_comapproof · cited by 5
- IsGaloisGroup.of_isFractionRingproof · cited by 5
- IsAlgebraic.restrictScalars_of_isIntegralproof · cited by 4