Theorems · Definition · commutative algebra
nonZeroDivisorsRight
(M₀ : Type u_1) → [inst : MonoidWithZero M₀] → Submonoid M₀
The collection of elements of a MonoidWithZero that are not right 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_nonZeroDivisorsproof · cited by 4
- nonZeroDivisorsLeft_eq_rightstatement · cited by 3
- mul_right_mem_nonZeroDivisorsRight_eq_zero_iffstatement and proof · cited by 3
- nonZeroDivisorsRight_eq_nonZeroDivisorsstatement · cited by 3
- isRightRegular_iff_mem_nonZeroDivisorsRightstatement · cited by 2
- le_nonZeroDivisors_iff_isRegularproof · cited by 2
- IsFractionRing.isFractionRing_of_isLocalizationproof · cited by 1
- MvPowerSeries.mem_nonZeroDivisorsRight_of_constantCoeffstatement and proof · cited by 1
- IsRightRegular.mem_nonZeroDivisorsRightstatement · cited by 1
- MvPowerSeries.monomial_mem_nonzeroDivisorsRightstatement and proof · cited by 1
- mul_cancel_right_mem_nonZeroDivisorsRightstatement and proof · cited by 1