Theorems · Theorem · group theory
Submonoid.LocalizationMap.map_eq_zero_iff
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoidWithZero N]
(f : S.LocalizationMap N) {m : M}, f m = 0 ↔ ∃ s, ↑s * m = 0- Cited by
- 3 results in Mathlib
- Foundations
- Depth 23 from the axioms · uses propext, Quot.sound
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 and proof · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- MulZeroClass.mul_zeroproof · cited by 2,091
- CommMonoidWithZerostatement and proof · cited by 913
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.map_zeroproof · cited by 5
Cited by3
Results whose statement or proof uses this declaration.
- IsLocalization.map_eq_zero_iffproof · cited by 12
- Submonoid.LocalizationMap.nonZeroDivisors_le_comapproof · cited by 2
- Submonoid.LocalizationMap.mk'_eq_zero_iffproof · cited by 1