Theorems · Inductive type · nonassociative algebras

RootPairing.IsIrreducible

{ι : Type u_1} →
  {R : Type u_2} →
    {M : Type u_3} →
      {N : Type u_4} →
        [inst : CommRing R] →
          [inst_1 : AddCommGroup M] →
            [inst_2 : Module R M] → [inst_3 : AddCommGroup N] → [inst_4 : Module R N] → RootPairing ι R M N → Prop

A root pairing is irreducible if it is non-trivial and contains no proper invariant submodules.

Defined in

Mathlib.LinearAlgebra.RootSystem.Irreducible

Cited by

35 results in Mathlib

Foundations

Depth 7 from the axioms · uses no axioms

Assumes

CommRingAddCommGroupModuleAddCommGroupModule