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Theorems · Theorem · linear algebra

Module.nontrivial_dual_iff

∀ (K : Type uK) {V : Type uV} [inst : CommSemiring K] [inst_1 : AddCommMonoid V] [inst_2 : Module K V]
  [Module.Projective K V], Nontrivial (Module.Dual K V) ↔ Nontrivial V
Defined in
Mathlib.LinearAlgebra.Dual.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommSemiringAddCommMonoidModuleModule.Projective
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RootPairing.IsIrreducible.mk' · cited by 1IsIrreducible.mk'Module · cited by 20661ModuleAddCommMonoid · cited by 12281AddCommMonoidCommSemiring · cited by 10911CommSemiringNontrivial · cited by 2416NontrivialModule.Dual · cited by 583Module.DualModule.Projective · cited by 82Module.ProjectiveModule.subsingleton_dual_iff · cited by 2Module.subsingleton_dual_…Module.nontrivial_dual_iffCITED BYCITES

Cites7

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