Theorems · Theorem · commutative algebra

Submodule.index_smul_le

∀ {R : Type u_1} {M : Type u_2} [inst : CommRing R] [inst_1 : AddCommGroup M] [inst_2 : Module R M] (I : Ideal R)
  {N : Submodule R M} [Finite (R ⧸ I)] (s : Finset M),
  Submodule.span R ↑s = N →
    (I • N).toAddSubgroup.index ≤ (Submodule.toAddSubgroup I).index ^ s.card * N.toAddSubgroup.index

Defined in

Mathlib.RingTheory.Ideal.Quotient.Index

Cited by

1 results in Mathlib

Foundations

Depth 95 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingAddCommGroupModuleFinite