Theorems · Theorem · commutative algebra
zero_notMem_nonZeroDivisors
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [Nontrivial M₀], 0 ∉ nonZeroDivisors M₀- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidWithZeroNontrivial
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- Nontrivialstatement and proof · cited by 2,416
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZerostatement and proof · cited by 456
- zero_notMem_nonZeroDivisorsLeftproof · cited by 1
Cited by6
Results whose statement or proof uses this declaration.
- nonZeroDivisors.ne_zeroproof · cited by 22
- IsLocalization.isDomain_of_le_nonZeroDivisorsproof · cited by 11
- map_le_nonZeroDivisors_of_injectiveproof · cited by 5
- FractionalIdeal.extendedHom_eq_zero_iffproof · cited by 4
- FractionalIdeal.num_eq_zero_iffproof · cited by 3
- FractionalIdeal.absNorm_eq_zero_iffproof · cited by 0