Theorems · Theorem · commutative algebra

Submodule.FG.restrictScalars_of_surjective

∀ {R : Type u_4} {A : Type u_5} {M : Type u_6} [inst : Semiring A] [inst_1 : AddCommMonoid M] [inst_2 : Module A M]
  {S : Submodule A M} [inst_3 : CommSemiring R] [inst_4 : Algebra R A] [inst_5 : Module R M]
  [inst_6 : IsScalarTower R A M], S.FG → Function.Surjective ⇑(algebraMap R A) → (Submodule.restrictScalars R S).FG

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

3 results in Mathlib

Foundations

Depth 55 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleCommSemiringAlgebraModuleIsScalarTower