Theorems · Theorem · commutative algebra
nonZeroDivisors.coe_ne_zero
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [Nontrivial M₀] (x : ↥(nonZeroDivisors M₀)), ↑x ≠ 0- Cited by
- 17 results in Mathlib
- Foundations
- Depth 18 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
- nonZeroDivisors.ne_zeroproof · cited by 22
Cited by17
Results whose statement or proof uses this declaration.
- IsDedekindDomain.HeightOneSpectrum.intValuation_ne_zero'proof · cited by 4
- isAddTorsion_iff_isTorsion_intproof · cited by 2
- ClassGroup.exists_minproof · cited by 1
- RingOfIntegers.isPrincipalIdealRing_of_isPrincipal_of_norm_le_of_isPrimeproof · cited by 1
- IsFractionRing.ideal_span_singleton_map_subsetproof · cited by 1
- FractionalIdeal.absNorm_span_singletonproof · cited by 1
- FractionalIdeal.abs_det_basis_changeproof · cited by 1
- IsLocalization.sec_snd_ne_zeroproof · cited by 1
- IsDedekindDomain.HeightOneSpectrum.valuationOfNeZeroToFun_eqproof · cited by 1
- ClassGroup.mk0_eq_mk0_inv_iffproof · cited by 1
- isAddTorsion_iff_isTorsion_natproof · cited by 1