Spectral mapping theorem

Let $𝐴$ be a $𝕂$ -monoid over an algebraically closed field $𝕂$ . Let $𝑎 \in 𝐴$ and $𝑝 (𝑥) \in 𝕂 [𝑥]$ . Then the spectra satisfy¹ #m/thm/falg

S p e c (𝑝 (𝑎)) = 𝑝 (S p e c (𝑎)) = {𝑝 (𝜆), 𝜆 \in S p e c (𝑎)}

Proof

#missing/proof

#state/develop | #lang/en | #SemBr

Footnotes