Bourbaki

Remark 6

Tag 024Y, permanent. Cite it as [Bourbaki, Tag 024Y].

Théories spectrales, chapter I, § 1. Spectres et caractères

Let A and B be unital algebras over K and φ:A→B\varphi : A\rightarrow B a unital morphism. For every x∈Ax\in A, one has SpB(φ(x))⊂_B(\varphi (x))\subset SpA(x)_A(x).

Bourbaki sets the proof directly after the statement, and the corpus does not separate them, so what is above is the statement and its proof together.

Cited by

Nothing.

Cites

Nothing.

Machine translation of the English, by gpt-5.4, gpt-5-6-mini, against glossary version 34. Not checked by a person. That model is a cut down version of the one the rest of this language was written by.