Example 6

Tag 001W, permanent. Cite it as [Bourbaki, Tag 001W].

Algebra, VIII, p. 26, § 2. The Structure of Modules of Finite Length

Let K be a commutative field of characteristic $p >0$ and G a $p$ -group (I, §6, No. 5, p. 76, Definition 9). The algebra K[G] of the group G over K (III, §2, No. 6, p. 446) is a local ring; its maximal ideal is the set of elements $(a_g)_{g\in G}$ of K[G] such that $\sum_{g\in G}a_g= 0$ (VIII, p. 41, Exercise 10).

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

I, §6, No. 5, p. 76, Definition 9 not in this corpus
III, §2, No. 6, p. 446
VIII, p. 41, Exercise 10