Theorems · Theorem · commutative algebra
AlgHom.Finite.of_surjective
∀ {R : Type u_1} {A : Type u_2} {B : Type u_3} [inst : CommRing R] [inst_1 : CommRing A] [inst_2 : CommRing B]
[inst_3 : Algebra R A] [inst_4 : Algebra R B] (f : A →ₐ[R] B), Function.Surjective ⇑f → f.Finite- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 1 results in Mathlib
- Foundations
- Depth 82 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites7
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
- AlgHomstatement and proof · cited by 3,236
- AlgHom.toRingHomproof · cited by 490
- AlgHom.Finitestatement · cited by 11
- RingHom.Finite.of_surjectiveproof · cited by 8
Cited by1
Results whose statement or proof uses this declaration.
- Algebra.ZariskisMainProperty.of_finiteType_of_weaklyQuasiFiniteAtproof · cited by 3