Theorems · Theorem · functional analysis

spectrum.smul_mem_smul_iff

∀ {R : Type u} {A : Type v} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A] {a : A} {s : R} {r : Rˣ},
  r • s ∈ spectrum R (r • a) ↔ s ∈ spectrum R a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Basic

Cited by

2 results in Mathlib

Foundations

Depth 22 from the axioms · uses propext, Quot.sound

Assumes

CommSemiringRingAlgebra