Theorems · Theorem · ring theory

linearIndepOn_isGroupLikeElem

∀ {R : Type u_2} {A : Type u_3} [inst : CommRing R] [IsDomain R] [inst_2 : AddCommGroup A] [inst_3 : Module R A]
  [inst_4 : Coalgebra R A] [Module.IsTorsionFree R A], LinearIndepOn R id {a | IsGroupLikeElem R a}

Group-like elements over a domain are linearly independent.

Defined in

Mathlib.RingTheory.Coalgebra.GroupLike

Cited by

3 results in Mathlib

Foundations

Depth 112 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingIsDomainAddCommGroupModuleCoalgebraModule.IsTorsionFree