Theorems · Theorem · nonassociative algebras

RootPairing.GeckConstruction.isNilpotent_f

∀ {ι : Type u_1} {R : Type u_2} {M : Type u_3} {N : Type u_4} [inst : CommRing R] [inst_1 : IsDomain R]
  [inst_2 : CharZero R] [inst_3 : AddCommGroup M] [inst_4 : Module R M] [inst_5 : AddCommGroup N] [inst_6 : Module R N]
  {P : RootPairing ι R M N} [inst_7 : P.IsCrystallographic] [P.IsReduced] {b : P.Base} [inst_9 : Fintype ι]
  [inst_10 : DecidableEq ι] (i : ↥b.support), IsNilpotent (RootPairing.GeckConstruction.f i)

Defined in: Mathlib.LinearAlgebra.RootSystem.GeckConstruction.Semisimple
Cited by: 1 results in Mathlib
Foundations: Depth 107 from the axioms · uses propext, Classical.choice, Quot.sound
Assumes: CommRing IsDomain CharZero AddCommGroup Module AddCommGroup Module RootPairing.IsCrystallographic RootPairing.IsReduced Fintype DecidableEq

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Mathlib declarations this one mentions in its statement or cites explicitly in its proof. Plumbing is filtered out.

Modulestatement and proof · cited by 20,661
CommRingstatement and proof · cited by 17,173
Finsetstatement · cited by 13,712
AddCommGroupstatement and proof · cited by 12,871
Fintypestatement and proof · cited by 7,736
Matrixstatement and proof · cited by 4,303
mul_oneproof · cited by 3,885
one_mulproof · cited by 2,841
IsDomainstatement and proof · cited by 2,196
MulZeroClass.mul_zeroproof · cited by 2,091
mul_assocproof · cited by 1,667
MulZeroClass.zero_mulproof · cited by 1,625

Cited by1

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RootPairing.GeckConstruction.trace_toEnd_eq_zeroproof · cited by 0