Theorems · Theorem · commutative algebra
unitsNonZeroDivisorsEquiv_apply
∀ {M₀ : Type u_1} [inst : MonoidWithZero M₀] (a : (↥(nonZeroDivisors M₀))ˣ),
unitsNonZeroDivisorsEquiv a = (↑(Units.map (nonZeroDivisors M₀).subtype)).toFun a- Cited by
- 2 results in Mathlib
- Foundations
- Depth 27 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.
- DFunLike.coestatement and proof · cited by 62,936
- Submonoidstatement · cited by 3,086
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- nonZeroDivisorsstatement and proof · cited by 895
- MonoidWithZerostatement and proof · cited by 456
- MonoidHom.toOneHomstatement · cited by 132
- OneHom.toFunstatement · cited by 132
- Units.mapstatement · cited by 95
- Submonoid.subtypestatement · cited by 26
- unitsNonZeroDivisorsEquivstatement and proof · cited by 6
Cited by2
Results whose statement or proof uses this declaration.
- NumberField.mixedEmbedding.fundamentalCone.integerSetToAssociates_eq_iffproof · cited by 0
- nonZeroDivisors.associated_coeproof · cited by 0