Theorems · Theorem · ring theory
linearIndep_groupLikeVal
∀ {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], LinearIndependent R GroupLike.valGroup-like elements over a domain are linearly independent.
- Defined in
- Mathlib.RingTheory.Coalgebra.GroupLike
- Cited by
- 0 results in Mathlib
- Foundations
- Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
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Cites12
Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.
- Modulestatement and proof · cited by 20,661
- CommRingstatement and proof · cited by 17,173
- AddCommGroupstatement and proof · cited by 12,871
- IsDomainstatement and proof · cited by 2,196
- Module.IsTorsionFreestatement and proof · cited by 600
- LinearIndependentstatement · cited by 560
- Coalgebrastatement and proof · cited by 112
- linearIndependent_equivproof · cited by 21
- GroupLikestatement · cited by 19
- GroupLike.valstatement · cited by 16
- GroupLike.valEquivproof · cited by 3
- linearIndepOn_isGroupLikeElemproof · cited by 3
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