Theorems · Definition · commutative algebra

Submodule.restrictScalarsLatticeHom

(S : Type u_1) →
  (R : Type u_2) →
    (M : Type u_3) →
      [inst : Semiring R] →
        [inst_1 : AddCommMonoid M] →
          [inst_2 : Semiring S] →
            [inst_3 : Module S M] →
              [inst_4 : Module R M] →
                [inst_5 : SMul S R] → [IsScalarTower S R M] → CompleteLatticeHom (Submodule R M) (Submodule S M)

If ring S acts on a ring R and M is a module over both (compatibly with this action) then we can turn an R-submodule into an S-submodule by forgetting the action of R.

Defined in

Mathlib.Algebra.Module.Submodule.RestrictScalars

Cited by

2 results in Mathlib

Foundations

Depth 71 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidSemiringModuleModuleSMulIsScalarTower