Bourbaki

Corollary 1

Tag 00MO, permanent. Cite it as [Bourbaki, Tag 00MO].

Algebra, VIII, p. 381, § 20. Linear Representations of Algebras

Every simple A-module of finite dimension over K is isomorphic to an A-submodule of Θ(A).

This follows from Theorem 1, b) because we have ΘE(A)≠0\Theta_E(A)\not= 0 for every nonzero A-module E.

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

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Cites

Transcribed from the printed edition, 2023, Springer Nature. Not translated.