Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.of_surjective_algHom
∀ {R : Type u_1} {S : Type u_2} {T : Type u_3} [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : CommRing T]
[inst_3 : Algebra R S] [inst_4 : Algebra R T] [Algebra.QuasiFinite R S] (f : S →ₐ[R] T),
Function.Surjective ⇑f → Algebra.QuasiFinite R T- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 7 results in Mathlib
- Foundations
- Depth 111 from the axioms · uses propext, Classical.choice, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites14
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
- IsScalarTowerproof · cited by 3,896
- AlgHomstatement and proof · cited by 3,236
- Module.Finiteproof · cited by 1,032
- AlgHom.toRingHomproof · cited by 490
- RingHom.toAlgebraproof · cited by 337
- Algebra.linearMapproof · cited by 157
- IsScalarTower.of_algebraMap_eq'proof · cited by 101
- AlgHom.comp_algebraMapproof · cited by 63
- Module.Finite.of_surjectiveproof · cited by 29
Cited by7
Results whose statement or proof uses this declaration.
- Algebra.QuasiFiniteAt.of_surjectiveOnStalksproof · cited by 3
- Algebra.QuasiFinite.of_forall_exists_mul_mem_rangeproof · cited by 3
- Algebra.QuasiFinite.iff_of_algEquivproof · cited by 1
- Algebra.ZariskisMainProperty.quasiFiniteAtproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_algHom_localizationproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.of_quasiFiniteAt_residueFieldproof · cited by 1
- Algebra.WeaklyQuasiFiniteAt.finite_locoalizationproof · cited by 0