Theorems · Theorem · commutative algebra
Algebra.QuasiFinite.of_forall_exists_mul_mem_range
∀ {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),
(∀ (x : T), ∃ s, IsUnit (f s) ∧ x * f s ∈ f.range) → Algebra.QuasiFinite R T- Defined in
- Mathlib.RingTheory.QuasiFinite.Basic
- Cited by
- 3 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.
Cites20
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
- IsUnitstatement and proof · cited by 1,602
- Subalgebrastatement · cited by 1,353
- RingHomClass.toRingHomproof · cited by 746
- AlgHom.toRingHomproof · cited by 490
- MonoidHomClass.toMonoidHomproof · cited by 294
- Localizationproof · cited by 270
- IsLocalization.mk'proof · cited by 218
- Submonoid.comapproof · cited by 179
Cited by3
Results whose statement or proof uses this declaration.
- Algebra.QuasiFiniteAt.baseChangeproof · cited by 4
- Algebra.ZariskisMainProperty.quasiFiniteAtproof · cited by 1
- Algebra.QuasiFiniteAt.of_leproof · cited by 0