Theorems · Definition · group theory
IsUnit.submonoid
(M : Type u_4) → [inst : Monoid M] → Submonoid M
The submonoid consisting of the units of a monoid
- Defined in
- Mathlib.Algebra.Group.Submonoid.Basic
- Cited by
- 56 results in Mathlib
- Foundations
- Depth 11 from the axioms · uses propext
- Assumes
- Monoid
Around this declaration
Dashed lines are statement dependencies; solid lines are citations in proofs.
Cites4
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Set.ofPredproof · cited by 6,101
- Monoidstatement and proof · cited by 3,887
- Submonoidstatement · cited by 3,086
- IsUnitproof · cited by 1,602
Cited by65
Results whose statement or proof uses this declaration.
- IsLocalization.atUnitsstatement and proof · cited by 10
- Submonoid.leftInvEquivstatement and proof · cited by 9
- IsLocalization.away_of_isUnit_of_bijectiveproof · cited by 6
- Ideal.ResidueField.liftₐstatement and proof · cited by 4
- IsLocalization.of_le_isUnit_of_bijectivestatement and proof · cited by 4
- Algebra.EssFiniteType.submonoidproof · cited by 4
- Submonoid.unitsTypeEquivIsUnitSubmonoidstatement and proof · cited by 3
- Ideal.ResidueField.liftstatement and proof · cited by 3
- Algebra.QuasiFinite.of_forall_exists_mul_mem_rangeproof · cited by 3
- Algebra.essFiniteType_iffproof · cited by 3
- Algebra.smoothLocus_eq_univ_iffproof · cited by 3
- IsFractionRing.self_iff_nonZeroDivisors_le_isUnitstatement and proof · cited by 3