Theorems · Definition · nonassociative algebras

LieModule.IsIrreducible

(R : Type u_1) →
  (L : Type u_2) →
    (M : Type u_3) →
      [inst : CommRing R] → [inst_1 : LieRing L] → [inst_2 : AddCommGroup M] → [Module R M] → [LieRingModule L M] → Prop

A nontrivial Lie module is irreducible if its only Lie submodules are ⊥ and ⊤.

Defined in

Mathlib.Algebra.Lie.Semisimple.Defs

Cited by

5 results in Mathlib

Foundations

Depth 80 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommRingLieRingAddCommGroupModuleLieRingModule