Theorems · Theorem · group theory
isUnit_iff_exists_inv
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {a : M}, IsUnit a ↔ ∃ b, a * b = 1- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 21 results in Mathlib
- Foundations
- Depth 10 from the axioms · uses no axioms
- Assumes
- MonoidIsDedekindFiniteMonoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites5
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Monoidstatement and proof · cited by 3,887
- IsUnitstatement and proof · cited by 1,602
- IsUnit.of_mul_eq_oneproof · cited by 43
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- IsUnit.exists_right_invproof · cited by 11
Cited by21
Results whose statement or proof uses this declaration.
- IsLocalization.AtPrime.isLocalRingproof · cited by 19
- isUnit_of_mul_isUnit_leftproof · cited by 12
- Ideal.mem_jacobson_botproof · cited by 4
- IsLocalization.AtPrime.isUnit_mk'_iffproof · cited by 3
- IsLocalization.mk'_mem_iffproof · cited by 3
- ValuationSubring.isMax_toLocalSubringproof · cited by 2
- RingHom.isIntegralElem_localization_at_leadingCoeffproof · cited by 2
- LocalSubring.exists_le_valuationSubringproof · cited by 2
- Polynomial.Monic.irreducible_iff_irreducible_map_fraction_mapproof · cited by 2
- HomogeneousLocalization.Away.isLocalization_mulproof · cited by 2
- Matrix.mem_subfield_of_mul_eq_one_of_mem_subfield_rightproof · cited by 1
- Matrix.isUnit_det_Jproof · cited by 1