Theorems · Definition · linear algebra

Submodule.baseChange

{R : Type u_1} →
  {M : Type u_2} →
    (A : Type u_3) →
      [inst : CommSemiring R] →
        [inst_1 : Semiring A] →
          [inst_2 : Algebra R A] →
            [inst_3 : AddCommMonoid M] → [inst_4 : Module R M] → Submodule R M → Submodule A (TensorProduct R A M)

If A is an R-algebra, any R-submodule p of an R-module M may be pushed forward to an A-submodule of A ⊗ M. This "base change" operation is also known as "extension of scalars".

Defined in

Mathlib.LinearAlgebra.TensorProduct.Tower

Cited by

36 results in Mathlib

Foundations

Depth 62 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringSemiringAlgebraAddCommMonoidModule