Theorems · Theorem · commutative algebra
mul_left_mem_nonZeroDivisorsLeft_eq_zero_iff
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {r x : M₀}, r ∈ nonZeroDivisorsLeft M₀ → (r * x = 0 ↔ x = 0)- Cited by
- 1 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidWithZero
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 · cited by 3,086
- MulZeroClass.mul_zeroproof · cited by 2,091
- MonoidWithZerostatement and proof · cited by 456
- nonZeroDivisorsLeftstatement and proof · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeffproof · cited by 1