Theorems · Theorem · commutative algebra
le_nonZeroDivisors_of_noZeroDivisors
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] [NoZeroDivisors M₀] {S : Submonoid M₀}, 0 ∉ S → S ≤ nonZeroDivisors M₀- Cited by
- 5 results in Mathlib
- Foundations
- Depth 24 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidWithZeroNoZeroDivisors
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 and proof · cited by 3,086
- nonZeroDivisorsstatement · cited by 895
- NoZeroDivisorsstatement and proof · cited by 545
- MonoidWithZerostatement and proof · cited by 456
- mem_nonZeroDivisors_of_ne_zeroproof · cited by 34
Cited by5
Results whose statement or proof uses this declaration.
- Ideal.primeCompl_le_nonZeroDivisorsproof · cited by 17
- map_le_nonZeroDivisors_of_injectiveproof · cited by 5
- powers_le_nonZeroDivisors_of_noZeroDivisorsproof · cited by 4
- IsField.localization_map_bijectiveproof · cited by 3
- Ideal.exists_ideal_over_prime_of_isIntegral_of_isDomainproof · cited by 2