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Theorems · Theorem · commutative algebra

Module.length_eq_one

∀ (R : Type u_1) (M : Type u_2) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [IsSimpleModule R M],
  Module.length R M = 1
Defined in
Mathlib.RingTheory.Length
Cited by
2 results in Mathlib
Foundations
Depth 69 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingAddCommGroupModuleIsSimpleModule
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

Module.length_eq_finrank · cited by 1Module.length_eq_finrankModule.length_eq_rank · cited by 1Module.length_eq_rankModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingENat · cited by 4985ENatIsSimpleModule · cited by 114IsSimpleModuleModule.length · cited by 56Module.lengthModule.length_eq_one_iff · cited by 4Module.length_eq_one_iffModule.length_eq_oneCITED BYCITES

Cites7

Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Cited by2

Results whose statement or proof uses this declaration.