Theorems · Definition · commutative algebra
nonZeroDivisorsLeft
(M₀ : Type u_1) → [inst : MonoidWithZero M₀] → Submonoid M₀
The collection of elements of a MonoidWithZero that are not left zero divisors form a
Submonoid.
- Cited by
- 26 results in Mathlib
- Foundations
- Depth 7 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.
- Set.ofPredproof · cited by 6,101
- Submonoidstatement · cited by 3,086
- MonoidWithZerostatement and proof · cited by 456
Cited by27
Results whose statement or proof uses this declaration.
- nonZeroDivisorsproof · cited by 895
- nonZeroDivisorsLeft_eq_nonZeroDivisorsstatement and proof · cited by 4
- isLeftRegular_iff_mem_nonZeroDivisorsLeftstatement · cited by 3
- nonZeroDivisorsLeft_eq_rightstatement · cited by 3
- biUnion_associatedPrimes_eq_compl_nonZeroDivisorsproof · cited by 2
- mul_left_mem_nonZeroDivisorsLeft_eq_zero_iffstatement and proof · cited by 1
- IsLeftRegular.mem_nonZeroDivisorsLeftstatement · cited by 1
- zero_notMem_nonZeroDivisorsLeftstatement and proof · cited by 1
- MvPowerSeries.mem_nonZeroDivisorsLeft_of_constantCoeffstatement and proof · cited by 1
- MvPowerSeries.monomial_mem_nonzeroDivisorsLeftstatement and proof · cited by 1
- OreLocalization.cardinalMkstatement and proof · cited by 1
- mul_cancel_left_mem_nonZeroDivisorsLeftstatement and proof · cited by 1