Theorems · Theorem · functional analysis

spectrum.zero_eq

∀ {𝕜 : Type u} {A : Type v} [inst : Field 𝕜] [inst_1 : Ring A] [inst_2 : Algebra 𝕜 A] [Nontrivial A], spectrum 𝕜 0 = {0}

Without the assumption Nontrivial A, then 0 : A would be invertible.

Defined in

Mathlib.Algebra.Algebra.Spectrum.Basic

Cited by

7 results in Mathlib

Foundations

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

Assumes

FieldRingAlgebraNontrivial