Theorems · Theorem · commutative algebra

Submodule.FG.of_restrictScalars

∀ {A : Type u_5} {M : Type u_6} [inst : Semiring A] [inst_1 : AddCommMonoid M] [inst_2 : Module A M] {S : Submodule A M}
  (R : Type u_7) [inst_3 : Semiring R] [inst_4 : Module R M] [inst_5 : SMul R A] [inst_6 : IsScalarTower R A M],
  (Submodule.restrictScalars R S).FG → S.FG

Defined in

Mathlib.RingTheory.Finiteness.Basic

Cited by

2 results in Mathlib

Foundations

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

Assumes

SemiringAddCommMonoidModuleSemiringModuleSMulIsScalarTower