Theorems · Theorem · commutative algebra

Module.IsTorsionFree.comap

∀ {R : Type u_1} {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]
  [inst_3 : Module R M] [inst_4 : Module S M] [Module.IsTorsionFree S M] (f : R → S),
  (∀ (r : R), IsRegular r → IsRegular (f r)) → (∀ (r : R) (m : M), f r • m = r • m) → Module.IsTorsionFree R M

Pullback an IsTorsionFree instance along a function preserving scalar multiplication and regular elements.

Defined in

Mathlib.Algebra.Module.Torsion.Free

Cited by

1 results in Mathlib

Foundations

Depth 14 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidModuleModuleModule.IsTorsionFree