Theorems · Theorem · functional analysis

QuasispectrumRestricts.rightInvOn

∀ {R : Type u_3} {S : Type u_4} {A : Type u_5} [inst : CommSemiring R] [inst_1 : CommSemiring S]
  [inst_2 : NonUnitalRing A] [inst_3 : Module R A] [inst_4 : Module S A] [inst_5 : Algebra R S] {a : A} {f : S → R},
  QuasispectrumRestricts a f → Set.RightInvOn f (⇑(algebraMap R S)) (quasispectrum S a)

f is a right inverse of algebraMap R S when restricted to quasispectrum S a.

Defined in

Mathlib.Algebra.Algebra.Spectrum.Quasispectrum

Cited by

6 results in Mathlib

Foundations

Depth 20 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringCommSemiringNonUnitalRingModuleModuleAlgebra