Theorems · Theorem · functional analysis

spectrum.subset_subalgebra

∀ {S : Type u_1} {R : Type u_2} {A : Type u_3} [inst : CommSemiring R] [inst_1 : Ring A] [inst_2 : Algebra R A]
  [inst_3 : SetLike S A] [inst_4 : SubringClass S A] [inst_5 : SMulMemClass S R A] {s : S} (a : ↥s),
  spectrum R ↑a ⊆ spectrum R a

Defined in

Mathlib.Algebra.Algebra.Spectrum.Basic

Cited by

2 results in Mathlib

Foundations

Depth 58 from the axioms · uses propext, Classical.choice, Quot.sound

Assumes

CommSemiringRingAlgebraSetLikeSubringClassSMulMemClass