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Theorems · Theorem · linear algebra

Module.rank_eq_zero_iff_isTorsion

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [IsDomain R] [inst_2 : AddCommGroup M] [inst_3 : Module R M],
  Module.rank R M = 0 ↔ Module.IsTorsion R M
Defined in
Mathlib.LinearAlgebra.Dimension.Torsion.Finite
Cited by
2 results in Mathlib
Foundations
Depth 88 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
CommRingIsDomainAddCommGroupModule
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Around this declaration

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Module.finrank_eq_zero_iff_isTorsion · cited by 0Module.finrank_eq_zero_if…rank_eq_zero_iff_isTorsion · cited by 0rank_eq_zero_iff_isTorsionModule · cited by 20661ModuleCommRing · cited by 17173CommRingAddCommGroup · cited by 12871AddCommGroupCardinal · cited by 2598CardinalIsDomain · cited by 2196IsDomainnonZeroDivisors · cited by 895nonZeroDivisorsModule.rank · cited by 496Module.rankModule.IsTorsion · cited by 23Module.IsTorsionModule.rank_eq_zero_iff_isTor…CITED BYCITES

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Cited by2

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