Theorems · Theorem · commutative algebra

isArtinian_of_tower

∀ (R : Type u_1) {S : Type u_2} {M : Type u_3} [inst : Semiring R] [inst_1 : Semiring S] [inst_2 : AddCommMonoid M]
  [inst_3 : SMul R S] [inst_4 : Module S M] [inst_5 : Module R M] [IsScalarTower R S M], IsArtinian R M → IsArtinian S M

If M / S / R is a scalar tower, and M / R is Artinian, then M / S is also Artinian.

Defined in

Mathlib.RingTheory.Artinian.Module

Cited by

6 results in Mathlib

Foundations

Depth 26 from the axioms · uses propext, Quot.sound

Assumes

SemiringSemiringAddCommMonoidSMulModuleModuleIsScalarTower