Theorems · Theorem · commutative algebra

smul_eq_zero

∀ {R : Type u_1} {M : Type u_3} [inst : Semiring R] [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {r : R} {m : M}
  [Module.IsTorsionFree R M] [IsCancelMulZero R], r • m = 0 ↔ r = 0 ∨ m = 0

Defined in

Mathlib.Algebra.Module.Torsion.Free

Cited by

40 results in Mathlib

Foundations

Depth 19 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleModule.IsTorsionFreeIsCancelMulZero