Theorems · Theorem · commutative algebra
Algebra.EssFiniteType.of_isLocalization
∀ {R : Type u_1} (S : Type u_2) [inst : CommRing R] [inst_1 : CommRing S] [inst_2 : Algebra R S] (M : Submonoid R)
[IsLocalization M S], Algebra.EssFiniteType R S- Defined in
- Mathlib.RingTheory.EssentialFiniteness
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 77 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.coeproof · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapproof · cited by 4,706
- Submonoidstatement and proof · cited by 3,086
- IsUnitproof · cited by 1,602
- IsLocalizationstatement and proof · cited by 636
- Algebra.adjoinproof · cited by 535
- Finset.coe_emptyproof · cited by 109
- IsLocalization.map_unitsproof · cited by 69
- Algebra.EssFiniteTypestatement · cited by 68
- IsLocalization.surjproof · cited by 29
Cited by5
Results whose statement or proof uses this declaration.
- Algebra.FormallyUnramified.isReduced_of_fieldproof · cited by 6
- IntermediateField.fg_top_iffproof · cited by 2
- Algebra.smoothLocus_eq_compl_support_interproof · cited by 2
- RingHom.EssFiniteType.holdsForLocalizationproof · cited by 1
- Algebra.essFiniteType_iff_exists_subalgebraproof · cited by 1