of_noZeroSMulDivisors — Mathlib

English

In a subtraction monoid, AddMonoid.IsTorsionFree is equivalent to NoZeroSMulDivisors over integers.

Русский

В subtraction моноиде IsTorsionFree эквивалентно NoZeroSMulDivisors над целыми.

LaTeX

$$$\text{IsTorsionFree} G \iff NoZeroSMulDivisors(\mathbb{Z}, G)$$$

Lean4

@[deprecated IsAddTorsionFree.of_noZeroSMulDivisors_nat (since := "2025-04-23")]
theorem of_noZeroSMulDivisors {M : Type*} [AddMonoid M] [NoZeroSMulDivisors ℕ M] : IsTorsionFree M :=
  isTorsionFree_iff_noZeroSMulDivisors_nat.2 ‹_›

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