Theorems · Theorem · functional analysis

SpectrumRestricts.algebraMap_image

∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : Semifield R] [inst_1 : Semifield S] [inst_2 : Ring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] {a : A} {f : S → R} [IsScalarTower R S A],
  SpectrumRestricts a f → ⇑(algebraMap R S) '' spectrum R a = spectrum S a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

12 results in Mathlib

Foundations

Depth 47 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

SemifieldSemifieldRingAlgebraAlgebraAlgebraIsScalarTower