Theorems · Theorem · commutative algebra
IsLocalization.finiteType_of_monoid_fg
∀ {R : Type u_1} [inst : CommRing R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommRing S] [inst_2 : Algebra R S]
[IsLocalization M S] [Monoid.FG ↥M], Algebra.FiniteType R S- Cited by
- 2 results in Mathlib
- Foundations
- Depth 79 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.
- CommRingstatement and proof · cited by 17,173
- Finsetproof · cited by 13,712
- Algebrastatement and proof · cited by 11,388
- Top.topproof · cited by 9,680
- SetLike.coeproof · cited by 8,199
- Submoduleproof · cited by 7,192
- Submonoidstatement and proof · cited by 3,086
- Submodule.spanproof · cited by 1,504
- IsLocalizationstatement and proof · cited by 636
- eq_top_iffproof · cited by 236
- Submonoid.closureproof · cited by 167
- Algebra.FiniteTypestatement · cited by 84
Cited by2
Results whose statement or proof uses this declaration.
- Algebra.exists_unramified_of_isUnramifiedAtproof · cited by 1
- RingHom.finiteType_holdsForLocalizationAwayproof · cited by 1