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Theorems · Theorem · commutative algebra

Module.length_eq_zero_of_subsingleton_ring

∀ {R : Type u_1} {M : Type u_2} [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [Subsingleton R],
  Module.length R M = 0
Defined in
Mathlib.RingTheory.Length
Cited by
1 results in Mathlib
Foundations
Depth 67 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes
RingAddCommGroupModuleSubsingleton
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Around this declaration

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

Module.length_of_free · cited by 3Module.length_of_freeModule · cited by 20661ModuleAddCommGroup · cited by 12871AddCommGroupRing · cited by 7463RingENat · cited by 4985ENatModule.length · cited by 56Module.lengthModule.subsingleton · cited by 20Module.subsingletonModule.length_eq_zero · cited by 9Module.length_eq_zeroModule.length_eq_zero_of_subs…CITED BYCITES

Cites7

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Cited by1

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