Theorems · Definition · ring theory

isotypicComponent

(R : Type u_2) →
  (M : Type u) →
    (S : Type u_4) →
      [inst : Ring R] →
        [inst_1 : AddCommGroup M] → [inst_2 : AddCommGroup S] → [inst_3 : Module R M] → [Module R S] → Submodule R M

If S is a simple R-module, the S-isotypic component in an R-module M is the sum of all submodules of M isomorphic to S.

Defined in

Mathlib.RingTheory.SimpleModule.Isotypic

Cited by

21 results in Mathlib

Foundations

Depth 64 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

RingAddCommGroupAddCommGroupModuleModule