Proposition 1
Tag 00P5, permanent. Cite it as [Bourbaki, Tag 00P5].
Algebra, VIII, p. 436, Appendix 1. Algebras without Unit Element
Every regular proper left (resp. right) ideal of A is contained in a regular maximal left (resp. right) ideal.
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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