Theorems · Theorem · commutative algebra
mk_mem_nonZeroDivisors_associates
∀ {M₀ : Type u_1} [inst : CommMonoidWithZero M₀] {a : M₀},
Associates.mk a ∈ nonZeroDivisors (Associates M₀) ↔ a ∈ nonZeroDivisors M₀- Cited by
- 2 results in Mathlib
- Foundations
- Depth 66 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- CommMonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites11
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- CommMonoidWithZerostatement and proof · cited by 913
- nonZeroDivisorsstatement and proof · cited by 895
- Associatesstatement and proof · cited by 210
- Associates.mkstatement and proof · cited by 137
- Associates.mk_ne_zeroproof · cited by 9
- mem_nonZeroDivisors_iff_rightproof · cited by 6
- Associates.mk_eq_zeroproof · cited by 6
- Associates.mk_mul_mkproof · cited by 5
- Associates.quot_mk_eq_mkproof · cited by 3
- Associates.mk_zeroproof · cited by 2
Cited by2
Results whose statement or proof uses this declaration.
- associatesNonZeroDivisorsEquiv_mk_mkstatement · cited by 0
- associatesNonZeroDivisorsEquiv_symm_mk_mkstatement · cited by 0