Corollary
Tag 009K, permanent. Cite it as [Bourbaki, Tag 009K].
Algebra, VIII, p. 143, § 8. Semisimple Rings
Let B be a ring. The following properties are equivalent:
(i) The ring B is simple.
(ii) The ring B is semisimple, and its center is a field.
(iii) The ring B is semisimple, and there exists only one class of B-simple modules.
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
Cites
Nothing.