Theorems · Theorem · commutative algebra

Module.length_of_free_of_finite

∀ (R : Type u_1) (M : Type u_2) [inst : Ring R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] [StrongRankCondition R]
  [Module.Free R M] [Module.Finite R M], Module.length R M = ↑(Module.finrank R M) * Module.length R R

Defined in: Mathlib.RingTheory.Length
Cited by: 0 results in Mathlib
Foundations: Depth 113 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: Ring AddCommGroup Module StrongRankCondition Module.Free Module.Finite

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Modulestatement and proof · cited by 20,661
AddCommGroupstatement and proof · cited by 12,871
Ringstatement and proof · cited by 7,463
ENatstatement and proof · cited by 4,985
Module.finrankstatement and proof · cited by 1,770
Module.Finitestatement and proof · cited by 1,032
Module.Freestatement and proof · cited by 597
StrongRankConditionstatement and proof · cited by 286
Module.lengthstatement and proof · cited by 56
Module.finrank_eq_rankproof · cited by 29
Cardinal.toENat_eq_natCastproof · cited by 6
Module.length_of_freeproof · cited by 3

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