Theorems · Theorem · commutative algebra
IsLocalization.mul_toInvSubmonoid
∀ {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] (m : ↥M), (algebraMap R S) ↑m * ↑((IsLocalization.toInvSubmonoid M S) m) = 1- Cited by
- 2 results in Mathlib
- Foundations
- Depth 35 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
- RingHomstatement · cited by 10,189
- Algebra.algebraMapstatement and proof · 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
- Submonoid.mapproof · cited by 190
- IsLocalization.toInvSubmonoidstatement · cited by 11
- IsLocalization.invSubmonoidstatement · cited by 10
Cited by2
Results whose statement or proof uses this declaration.
- IsLocalization.surj''proof · cited by 2
- IsLocalization.smul_toInvSubmonoidproof · cited by 0