Theorems · Theorem · commutative algebra
mem_nonZeroDivisors_iff_right
∀ {M₀ : Type u_1} [inst : CommMonoidWithZero M₀] {r : M₀}, r ∈ nonZeroDivisors M₀ ↔ ∀ (x : M₀), x * r = 0 → x = 0- Cited by
- 6 results in Mathlib
- Foundations
- Depth 65 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement and proof · cited by 3,086
- CommMonoidWithZerostatement and proof · cited by 913
- nonZeroDivisorsstatement · cited by 895
- nonZeroDivisorsRight_eq_nonZeroDivisorsproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- RatFunc.taylor_mem_nonZeroDivisorsproof · cited by 2
- mk_mem_nonZeroDivisors_associatesproof · cited by 2
- QuadraticAlgebra.star_mem_nonZeroDivisorsproof · cited by 2
- Matrix.det_detproof · cited by 1
- IsFractionRing.isFractionRing_of_isLocalizationproof · cited by 1
- Module.AEval.isTorsion_of_aeval_eq_zeroproof · cited by 1