Theorems · Theorem · functional analysis

spectrum.algebraMap_mem_iff

∀ (S : Type u_1) {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : CommSemiring S] [inst_2 : Ring A]
  [inst_3 : Algebra R S] [inst_4 : Algebra R A] [inst_5 : Algebra S A] [IsScalarTower R S A] {a : A} {r : R},
  (algebraMap R S) r ∈ spectrum S a ↔ r ∈ spectrum R a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Basic

Cited by

6 results in Mathlib

Foundations

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

Assumes

CommSemiringCommSemiringRingAlgebraAlgebraAlgebraIsScalarTower