Theorems · Theorem · nonassociative algebras

RootPairing.isIrreducible_iff_invtRootSubmodule

∀ {ι : Type u_1} {M : Type u_3} {N : Type u_4} [inst : AddCommGroup M] [inst_1 : AddCommGroup N] {K : Type u_5}
  [inst_2 : Field K] [inst_3 : Module K M] [inst_4 : Module K N] [Nontrivial M] (P : RootPairing ι K M N),
  P.IsIrreducible ↔ IsSimpleOrder ↥P.invtRootSubmodule

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

1 results in Mathlib

Foundations

Depth 98 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

AddCommGroupAddCommGroupFieldModuleModuleNontrivial