Theorems · Theorem · linear algebra

Module.finrank_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]
  [StrongRankCondition R] [Module.Finite R M], Module.finrank R M = 0 ↔ Module.IsTorsion R M

The StrongRankCondition is automatic. See commRing_strongRankCondition.

Defined in: Mathlib.LinearAlgebra.Dimension.Torsion.Finite
Cited by: 0 results in Mathlib
Foundations: Depth 102 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain AddCommGroup Module StrongRankCondition Module.Finite

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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.finrankstatement and proof · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
StrongRankConditionstatement and proof · cited by 286
Module.IsTorsionstatement · cited by 23
Module.rank_eq_zero_iff_isTorsionproof · cited by 2

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