Theorems · Theorem · group theory
eq_zero_of_mul_eq_self_right
∀ {M₀ : Type u_1} {a b : M₀} [inst : MulZeroOneClass M₀] [IsLeftCancelMulZero M₀], b ≠ 1 → a * b = a → a = 0An element of a left-cancellative MulZeroOneClass fixed by right multiplication by
an element other than one must be zero.
- Defined in
- Mathlib.Algebra.GroupWithZero.Basic
- Cited by
- 1 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.
- mul_oneproof · cited by 3,885
- MulZeroOneClassstatement and proof · cited by 184
- IsLeftCancelMulZerostatement and proof · cited by 48
- mul_left_cancel₀proof · cited by 47
Cited by1
Results whose statement or proof uses this declaration.
- IsDiscreteValuationRing.irreducible_of_span_eq_maximalIdealproof · cited by 2