Theorems · Theorem · group theory
Submonoid.LocalizationMap.map_zero
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoidWithZero N]
(f : S.LocalizationMap N), f 0 = 0- Cited by
- 5 results in Mathlib
- Foundations
- Depth 21 from the axioms · uses propext, Quot.sound
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
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
- MulZeroClass.zero_mulproof · cited by 1,625
- map_mulproof · cited by 1,137
- CommMonoidWithZerostatement and proof · cited by 913
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.surjproof · cited by 15
Cited by5
Results whose statement or proof uses this declaration.
- Submonoid.LocalizationMap.map_eq_zero_iffproof · cited by 3
- Submonoid.LocalizationMap.noZeroDivisorsproof · cited by 1
- Submonoid.LocalizationMap.mk'_zeroproof · cited by 1
- Submonoid.IsLocalizationMap.map_zeroproof · cited by 0