Theorems · Definition · commutative algebra

Submodule.restrictScalarsEmbedding

(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 ↪o Submodule S M

restrictScalars S is an embedding of the lattice of R-submodules into the lattice of S-submodules.

Defined in

Mathlib.Algebra.Module.Submodule.RestrictScalars

Cited by

5 results in Mathlib

Foundations

Depth 25 from the axioms · uses propext, Quot.sound

Assumes

SemiringAddCommMonoidSemiringModuleModuleSMulIsScalarTower