Theorems · Theorem · commutative algebra
IsLeftRegular.mem_nonZeroDivisorsLeft
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {r : M₀}, IsLeftRegular r → r ∈ nonZeroDivisorsLeft M₀- 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.
Cites5
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
- IsLeftRegularstatement and proof · cited by 97
- nonZeroDivisorsLeftstatement · cited by 26
- IsLeftRegular.mul_left_eq_zero_iffproof · cited by 3
Cited by1
Results whose statement or proof uses this declaration.
- IsRegular.mem_nonZeroDivisorsproof · cited by 2