Theorems · Definition · commutative algebra
unitsNonZeroDivisorsEquiv
{M₀ : Type u_1} → [inst : MonoidWithZero M₀] → (↥(nonZeroDivisors M₀))ˣ ≃* M₀ˣThe units of the monoid of non-zero divisors of M₀ are equivalent to the units of M₀.
- Cited by
- 6 results in Mathlib
- Foundations
- Depth 26 from the axioms · uses propext, Quot.sound
- Assumes
- MonoidWithZero
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.
- MonoidHomproof · cited by 3,629
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- Units.valproof · cited by 1,966
- MulEquivstatement · cited by 1,142
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZerostatement and proof · cited by 456
- MonoidHom.toOneHomproof · cited by 132
- OneHom.toFunproof · cited by 132
- Units.mapproof · cited by 95
- Submonoid.subtypeproof · cited by 26
Cited by6
Results whose statement or proof uses this declaration.
- unitsNonZeroDivisorsEquiv_applystatement and proof · cited by 2
- val_unitsNonZeroDivisorsEquiv_symm_apply_coestatement and proof · cited by 1
- val_inv_unitsNonZeroDivisorsEquiv_symm_apply_coestatement and proof · cited by 1
- nonZeroDivisors.associated_coeproof · cited by 0
- NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iffproof · cited by 0