Theorems · Theorem · group theory
IsUnit.of_mul_eq_one_right
∀ {M : Type u_1} [inst : Monoid M] [IsDedekindFiniteMonoid M] {b : M} (a : M), a * b = 1 → IsUnit b- Defined in
- Mathlib.Algebra.Group.Units.Defs
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 9 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 · cited by 1,602
- IsUnit.of_mul_eq_oneproof · cited by 43
- IsDedekindFiniteMonoidstatement and proof · cited by 23
- IsDedekindFiniteMonoid.mul_eq_one_symmproof · cited by 5
Cited by5
Results whose statement or proof uses this declaration.
- isUnit_iff_exists_inv'proof · cited by 8
- Submodule.range_unitsToPicproof · cited by 4
- Module.End.exists_isNilpotent_isSemisimple_of_separable_of_dvd_powproof · cited by 1
- Polynomial.resultant_dvd_leadingCoeff_powproof · cited by 1
- divisor_closure_eq_closureproof · cited by 0