Theorems · Theorem · group theory
eq_zero_of_mul_eq_self_left
∀ {M₀ : Type u_1} {a b : M₀} [inst : MulZeroOneClass M₀] [IsRightCancelMulZero M₀], b ≠ 1 → b * a = a → a = 0An element of a right-cancellative MulZeroOneClass fixed by left multiplication by
an element other than one must be zero.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 5 results in Mathlib
- Foundations
- Depth 13 from the axioms · uses propext, Classical.choice, Quot.sound
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.
- one_mulproof · cited by 2,841
- MulZeroOneClassstatement and proof · cited by 184
- IsRightCancelMulZerostatement and proof · cited by 33
- mul_right_cancel₀proof · cited by 22
Cited by5
Results whose statement or proof uses this declaration.
- MulChar.sum_eq_zero_of_ne_oneproof · cited by 9
- AddChar.sum_eq_iteproof · cited by 3
- AddChar.sum_eq_zero_of_ne_oneproof · cited by 2
- DirichletCharacter.sum_characters_eq_zeroproof · cited by 1
- Nat.Coprime.mul_add_mul_ne_mulproof · cited by 1