Theorems · Theorem · commutative algebra
isRightRegular_of_mul_eq_one
∀ {R : Type u_1} [inst : Monoid R] {a b : R}, a * b = 1 → IsRightRegular aAn element admitting a right inverse is right-regular.
- Defined in
- Mathlib.Algebra.Regular.Basic
- Cited by
- 2 results in Mathlib
- Foundations
- Depth 7 from the axioms · uses no axioms
- Assumes
- Monoid
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
- IsRightRegularstatement and proof · cited by 93
- IsRegular.rightproof · cited by 19
- isRegular_oneproof · cited by 8
- IsRightRegular.of_mulproof · cited by 7
Cited by2
Results whose statement or proof uses this declaration.
- Units.isRegularproof · cited by 2
- IsDedekindFiniteMonoid.iff_isRightRegular_of_mul_eq_oneproof · cited by 0