Theorems · Theorem · commutative algebra
RingHom.Finite.of_surjective
∀ {A : Type u_1} {B : Type u_2} [inst : CommRing A] [inst_1 : CommRing B] (f : A →+* B),
Function.Surjective ⇑f → f.Finite- Defined in
- Mathlib.RingTheory.Finiteness.Basic
- Cited by
- 8 results in Mathlib
- Foundations
- Depth 81 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
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
- RingHomstatement and proof · cited by 10,189
- Algebra.linearMapproof · cited by 157
- RingHom.Finitestatement · cited by 48
- Module.Finite.of_surjectiveproof · cited by 29
Cited by8
Results whose statement or proof uses this declaration.
- AlgebraicGeometry.Scheme.Hom.finrank_SpecMap_eq_finrankproof · cited by 6
- RingEquiv.finiteproof · cited by 5
- RingHom.finite_respectsIsoproof · cited by 3
- AlgHom.Finite.of_surjectiveproof · cited by 1
- RingHom.finrank_comp_right_of_bijectiveproof · cited by 1
- Localization.exists_finite_awayMapₐ_of_surjective_awayMapₐproof · cited by 1
- Algebra.not_isStronglyTranscendental_of_weaklyQuasiFiniteAtproof · cited by 1
- RingHom.surjective_iff_epi_and_finiteproof · cited by 1