Theorems · Definition · group theory
WithZero.unitsWithZeroEquiv
{α : Type u_1} → [inst : Group α] → (WithZero α)ˣ ≃* αAny group is isomorphic to the units of itself adjoined with 0.
- Defined in
- Mathlib.Algebra.GroupWithZero.WithZero
- Cited by
- 4 results in Mathlib
- Foundations
- Depth 27 from the axioms · uses propext, Classical.choice, Quot.sound
- Assumes
- Group
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.
- Groupstatement and proof · cited by 6,238
- Unitsstatement and proof · cited by 2,804
- MulEquivstatement · cited by 1,142
- WithZerostatement and proof · cited by 586
- WithZero.coeproof · cited by 186
- Units.mk0proof · cited by 181
- WithZero.unzeroproof · cited by 38
- WithZero.coe_ne_zeroproof · cited by 11
Cited by7
Results whose statement or proof uses this declaration.
- WithZero.logEquivproof · cited by 4
- OrderMonoidIso.unitsWithZeroproof · cited by 4
- WithZero.expEquivproof · cited by 3
- WithZero.unitsWithZeroEquiv_applystatement and proof · cited by 1
- WithZero.unitsWithZeroEquiv_symm_applystatement and proof · cited by 0
- WithZero.coe_unitsWithZeroEquiv_eq_units_valstatement · cited by 0
- IsDedekindDomain.HeightOneSpectrum.exists_valuation_sub_lt_of_integerproof · cited by 0