Theorems · Theorem · commutative algebra
mul_right_mem_nonZeroDivisors_eq_zero_iff
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {r x : M₀}, r ∈ nonZeroDivisors M₀ → (x * r = 0 ↔ x = 0)- Cited by
- 6 results in Mathlib
- Foundations
- Depth 16 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
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZerostatement and proof · cited by 456
- mul_right_mem_nonZeroDivisorsRight_eq_zero_iffproof · cited by 3
Cited by6
Results whose statement or proof uses this declaration.
- mul_left_mem_nonZeroDivisors_eq_zero_iffproof · cited by 4
- RatFunc.taylor_mem_nonZeroDivisorsproof · cited by 2
- Polynomial.comp_C_mul_X_eq_zero_iffproof · cited by 2
- IsAlgebraic.of_aevalproof · cited by 1
- mul_right_coe_nonZeroDivisors_eq_zero_iffproof · cited by 0
- Matrix.det_eq_zero_of_mulVec_eq_zero_of_mem_nonZeroDivisorsproof · cited by 0