Theorems · Theorem · commutative algebra
Algebra.isIntegral_def
∀ {R : Type u_1} {A : Type u_3} [inst : CommRing R] [inst_1 : Ring A] [inst_2 : Algebra R A],
Algebra.IsIntegral R A ↔ ∀ (x : A), IsIntegral R x- Cited by
- 6 results in Mathlib
- Foundations
- Depth 71 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
- Ringstatement and proof · cited by 7,463
- IsIntegralstatement and proof · cited by 427
- Algebra.IsIntegralstatement and proof · cited by 224
Cited by6
Results whose statement or proof uses this declaration.
- finite_of_finite_type_of_isJacobsonRingproof · cited by 4
- Algebra.isAlgebraic_iff_isIntegralproof · cited by 3
- le_integralClosure_iff_isIntegralproof · cited by 3
- Algebra.IsIntegral.of_surjectiveproof · cited by 2
- PrimeSpectrum.isIntegral_of_isClosedMap_comap_mapRingHomproof · cited by 1
- Subalgebra.isIntegral_iffproof · cited by 0