Theorems · Theorem · commutative algebra
mem_nonZeroDivisorsLeft_iff
∀ (M₀ : Type u_1) [inst : MonoidWithZero M₀] {x : M₀}, x ∈ nonZeroDivisorsLeft M₀ ↔ ∀ (y : M₀), x * y = 0 → y = 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.
Cites3
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- MonoidWithZerostatement and proof · cited by 456
- nonZeroDivisorsLeftstatement · cited by 26
Cited by1
Results whose statement or proof uses this declaration.
- MonomialOrder.mem_nonZeroDivisors_of_leadingCoeff_mem_nonZeroDivisorsproof · cited by 1