Theorems · Theorem · commutative algebra
Subalgebra.isIntegral_iff
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B] (S : Subalgebra R B),
Algebra.IsIntegral R ↥S ↔ ∀ x ∈ S, IsIntegral R x- Cited by
- 0 results in Mathlib
- Foundations
- Depth 114 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites10
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
- Subalgebrastatement and proof · cited by 1,353
- IsIntegralstatement · cited by 427
- Subtype.val_injectiveproof · cited by 232
- Algebra.IsIntegralstatement · cited by 224
- Subalgebra.valproof · cited by 104
- isIntegral_algHom_iffproof · cited by 15
- Algebra.isIntegral_defproof · cited by 6
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