Theorems · Theorem · commutative algebra
Algebra.IsIntegral.of_surjective
∀ {R : Type u_1} [inst : CommRing R] {A : Type u_5} {B : Type u_6} [inst_1 : Ring A] [inst_2 : Ring B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] [Algebra.IsIntegral R A] (f : A →ₐ[R] B),
Function.Surjective ⇑f → Algebra.IsIntegral R BHomomorphic image of an integral algebra is an integral algebra.
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 113 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
- Ringstatement and proof · cited by 7,463
- AlgHomstatement and proof · cited by 3,236
- IsIntegralproof · cited by 427
- Algebra.IsIntegralstatement and proof · cited by 224
- IsIntegral.mapproof · cited by 22
- Algebra.isIntegral_defproof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.isIntegral_of_surjectiveproof · cited by 3
- Algebra.exists_etale_isIdempotentElem_forall_liesOver_eq_aux₂proof · cited by 1