Proposition 6
Tag 00PH, permanent. Cite it as [Bourbaki, Tag 00PH].
Algebra, VIII, p. 441, Appendix 1. Algebras without Unit Element
The radical of the algebra A is the intersection of the annihilators of the simple pseudomodules. It is, in particular, a two-sided ideal of A.
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.
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Cites
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