Theorems · Theorem · commutative algebra
mul_right_mem_nonZeroDivisorsRight_eq_zero_iff
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {r x : M₀}, r ∈ nonZeroDivisorsRight M₀ → (x * r = 0 ↔ x = 0)- Cited by
- 3 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.zero_mulproof · cited by 1,625
- MonoidWithZerostatement and proof · cited by 456
- nonZeroDivisorsRightstatement and proof · cited by 26
Cited by3
Results whose statement or proof uses this declaration.
- mul_right_mem_nonZeroDivisors_eq_zero_iffproof · cited by 6
- Submonoid.LocalizationMap.nonZeroDivisors_le_comapproof · cited by 2
- MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeffproof · cited by 1