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Theorems · Theorem · commutative algebra

LinearMap.isNilpotent_mulLeft_iff

∀ (R : Type u_1) {A : Type v} [inst : CommSemiring R] [inst_1 : Semiring A] [inst_2 : Algebra R A] (a : A),
  IsNilpotent (LinearMap.mulLeft R a) ↔ IsNilpotent a
Defined in
Mathlib.RingTheory.Nilpotent.Lemmas
Cited by
1 results in Mathlib
Foundations
Depth 29 from the axioms · uses propext, Quot.sound
Assumes
CommSemiringSemiringAlgebra
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Around this declaration

Dashed lines are statement dependencies; solid lines are citations in proofs.

LieAlgebra.ad_nilpotent_of_nilpotent · cited by 2LieAlgebra.ad_nilpotent_o…RingHom.id · cited by 18349RingHom.idSemiring · cited by 13802SemiringAlgebra · cited by 11388AlgebraCommSemiring · cited by 10911CommSemiringLinearMap · cited by 10215LinearMapIsNilpotent · cited by 248IsNilpotentLinearMap.mulLeft · cited by 34LinearMap.mulLeftLinearMap.pow_mulLeft · cited by 2LinearMap.pow_mulLeftLinearMap.isNilpotent_mulLeft…CITED BYCITES

Cites8

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

Cited by1

Results whose statement or proof uses this declaration.