Theorems · Theorem · group theory
Submonoid.LocalizationMap.noZeroDivisors
∀ {M : Type u_1} [inst : CommMonoidWithZero M] {S : Submonoid M} {N : Type u_2} [inst_1 : CommMonoidWithZero N]
(f : S.LocalizationMap N) [NoZeroDivisors M], NoZeroDivisors N- Cited by
- 1 results in Mathlib
- Foundations
- Depth 67 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.coeproof · cited by 62,936
- Submonoidstatement and proof · cited by 3,086
- CommMonoidWithZerostatement and proof · cited by 913
- nonZeroDivisorsproof · cited by 895
- NoZeroDivisorsstatement and proof · cited by 545
- Submonoid.LocalizationMapstatement and proof · cited by 147
- Submonoid.LocalizationMap.map_unitsproof · cited by 46
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
- Submonoid.LocalizationMap.surjproof · cited by 15
- IsUnit.mul_left_eq_zeroproof · cited by 10
- mul_mem_nonZeroDivisorsproof · cited by 7
- Submonoid.LocalizationMap.map_zeroproof · cited by 5
Cited by1
Results whose statement or proof uses this declaration.
- IsLocalization.noZeroDivisorsproof · cited by 0