Theorems · Theorem · commutative algebra
IsRegular.mem_nonZeroDivisors
∀ {M₀ : Type u_2} [inst : MonoidWithZero M₀] {r : M₀}, IsRegular r → r ∈ nonZeroDivisors M₀- Cited by
- 2 results in Mathlib
- Foundations
- Depth 16 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidWithZero
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites8
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Submonoidstatement · cited by 3,086
- nonZeroDivisorsstatement · cited by 895
- MonoidWithZerostatement and proof · cited by 456
- IsRegularstatement and proof · cited by 116
- IsRegular.leftproof · cited by 39
- IsRegular.rightproof · cited by 19
- IsLeftRegular.mem_nonZeroDivisorsLeftproof · cited by 1
- IsRightRegular.mem_nonZeroDivisorsRightproof · cited by 1
Cited by2
Results whose statement or proof uses this declaration.
- MonomialOrder.degree_smul_of_isRegularproof · cited by 1
- Ideal.eq_top_of_mk_tensor_eq_oneproof · cited by 0