Theorems · Theorem · commutative algebra
IsLocalization.toInvSubmonoid_surjective
∀ {R : Type u_1} [inst : CommRing R] (M : Submonoid R) (S : Type u_2) [inst_1 : CommRing S] [inst_2 : Algebra R S]
[inst_3 : IsLocalization M S], Function.Surjective ⇑(IsLocalization.toInvSubmonoid M S)- Cited by
- 2 results in Mathlib
- Foundations
- Depth 34 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 · cited by 62,936
- CommRingstatement and proof · cited by 17,173
- Algebrastatement and proof · cited by 11,388
- Algebra.algebraMapproof · cited by 4,706
- MonoidHomstatement · cited by 3,629
- Submonoidstatement and proof · cited by 3,086
- IsLocalizationstatement and proof · cited by 636
- MonoidHomClass.toMonoidHomproof · cited by 294
- Equiv.surjectiveproof · cited by 198
- MulEquiv.toEquivproof · cited by 126
- IsLocalization.toInvSubmonoidstatement · cited by 11
- IsLocalization.invSubmonoidstatement · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.finiteType_of_monoid_fgproof · cited by 2
- IsLocalization.mem_invSubmonoid_iff_exists_mk'proof · cited by 0