Theorems · Theorem · group theory
Submonoid.LocalizationMap.surj
∀ {M : Type u_1} [inst : CommMonoid M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoid N]
(f : S.LocalizationMap N) (z : N), ∃ x, z * f ↑x.2 = f x.1- Cited by
- 15 results in Mathlib
- Foundations
- Depth 20 from the axioms · uses propext, Quot.sound
- Assumes
- CommMonoidCommMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites6
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- DFunLike.coestatement · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- CommMonoidstatement and proof · cited by 2,264
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.IsLocalizationMap.surjproof · cited by 8
- Submonoid.LocalizationMap.isLocalizationMapproof · cited by 5
Cited by16
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.secproof · cited by 26
- Submonoid.LocalizationMap.map_zeroproof · cited by 5
- Submonoid.LocalizationMap.sec_specproof · cited by 2
- Submonoid.LocalizationMap.surj₂proof · cited by 2
- Submonoid.LocalizationMap.isCancelMulZeroproof · cited by 2
- Submonoid.LocalizationMap.nonZeroDivisors_le_comapproof · cited by 2
- Submonoid.LocalizationMap.map_isRegularproof · cited by 2
- Submonoid.LocalizationMap.map_primeproof · cited by 1
- Submonoid.LocalizationMap.uniqueFactorizationMonoidproof · cited by 1
- Submonoid.LocalizationMap.lift_injective_iffproof · cited by 1
- Submonoid.LocalizationMap.lift_surjective_iffproof · cited by 1
- Submonoid.LocalizationMap.map_dvd_mapproof · cited by 1