Theorems · Theorem · commutative algebra

Submodule.FG.restrictScalars

∀ {R : Type u_1} [inst : Semiring R] {M : Type u_2} [inst_1 : AddCommMonoid M] [inst_2 : Module R M] {A : Type u_3}
  [inst_3 : Semiring A] [inst_4 : Module R A] [inst_5 : Module A M] [inst_6 : IsScalarTower R A M] {S : Submodule A M}
  [Module.Finite R A], S.FG → (Submodule.restrictScalars R S).FG

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

2 results in Mathlib

Foundations

Depth 84 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemiringAddCommMonoidModuleSemiringModuleModuleIsScalarTowerModule.Finite