Theorems · Definition · commutative algebra

Submodule.restrictScalars

(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] → Submodule R M → Submodule S M

V.restrictScalars S is the S-submodule of the S-module given by restriction of scalars, corresponding to V, an R-submodule of the original R-module.

Defined in

Mathlib.Algebra.Module.Submodule.RestrictScalars

Cited by

180 results in Mathlib

Foundations

Depth 15 from the axioms, rests on 112 definitions · uses no axioms

Assumes

SemiringAddCommMonoidSemiringModuleModuleSMulIsScalarTower