Theorems · Definition · commutative algebra

Submodule.pointwiseSetSMul

{R : Type u_2} →
  {M : Type u_3} →
    [inst : Semiring R] →
      [inst_1 : AddCommMonoid M] →
        [inst_2 : Module R M] →
          {S : Type u_4} → [inst_3 : Monoid S] → [DistribMulAction S M] → SMul (Set S) (Submodule R M)

Let s ⊆ R be a set and N ≤ M be a submodule, then s • N is the smallest submodule containing all r • n where r ∈ s and n ∈ N.

Defined in

Mathlib.Algebra.Module.Submodule.Pointwise

Cited by

30 results in Mathlib

Foundations

Depth 17 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidModuleMonoidDistribMulAction