Theorems · Theorem · commutative algebra
Algebra.isIntegral_of_surjective
∀ {R : Type u_1} {B : Type u_3} [inst : CommRing R] [inst_1 : Ring B] [inst_2 : Algebra R B],
Function.Surjective ⇑(algebraMap R B) → Algebra.IsIntegral R B- Cited by
- 3 results in Mathlib
- Foundations
- Depth 132 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites9
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
- Ringstatement and proof · cited by 7,463
- Algebra.algebraMapstatement and proof · cited by 4,706
- Algebra.IsIntegralstatement · cited by 224
- Algebra.ofIdproof · cited by 166
- Algebra.IsIntegral.of_surjectiveproof · cited by 2
Cited by3
Results whose statement or proof uses this declaration.
- IsTranscendenceBasis.mvPolynomialproof · cited by 3
- exists_isTranscendenceBasis_and_isSeparable_of_perfectFieldproof · cited by 0