Theorems · Theorem · group theory
IsUnit.of_mul_eq_one
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {a : M} (b : M), a * b = 1 → IsUnit a- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 43 results in Mathlib
- Foundations
- Depth 8 from the axioms · uses no axioms
- Assumes
- MonoidIsDedekindFiniteMonoid
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.
- Monoidstatement and proof · cited by 3,887
- IsUnitstatement · cited by 1,602
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- Units.mkOfMulEqOneproof · cited by 15
Cited by43
Results whose statement or proof uses this declaration.
- IsPrimitiveRoot.isUnitproof · cited by 22
- isUnit_iff_exists_invproof · cited by 21
- IsUnit.of_mul_eq_one_rightproof · cited by 5
- Polynomial.Monic.isPrimitiveproof · cited by 4
- StandardEtalePair.hasMap_Xproof · cited by 3
- Polynomial.irreducible_of_monicproof · cited by 3
- IsNilpotent.isUnit_quotient_mk_iffproof · cited by 3
- LinearEquiv.isUnit_det'proof · cited by 3
- isCoprime_selfproof · cited by 3
- isCoprime_zero_leftproof · cited by 3
- isUnit_of_associated_mulproof · cited by 3
- Ideal.isPrincipal_of_isPrincipal_isLocalizationAway_of_primeproof · cited by 2