Theorems · Theorem · commutative algebra

Submodule.restrictScalars_mem

∀ (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] [inst_6 : IsScalarTower S R M] (V : Submodule R M)
  (m : M), m ∈ Submodule.restrictScalars S V ↔ m ∈ V

Defined in

Mathlib.Algebra.Module.Submodule.RestrictScalars

Cited by

14 results in Mathlib

Foundations

Depth 16 from the axioms · uses no axioms

Assumes

SemiringAddCommMonoidSemiringModuleModuleSMulIsScalarTower