Bourbaki

Theorem 1

Tag 0DNK, permanent. Cite it as [Bourbaki, Tag 0DNK].

Algebra, chapter IX, § 9. Algèbres de Clifford

Suppose that the AA-module EE admits a basis (xi)i∈L(x_i)_{i \in L}, the set of indices LL being endowed with a total ordering. For every finite subset HH of LL, put xH=ρ(xh1)ρ(xh2)…ρ(xhq)x_H = \rho(x_{h_1}) \rho(x_{h_2}) \ldots \rho(x_{h_q}), where (h1,…,hq)(h_1, \ldots, h_q) is the strictly increasing sequence of the elements of HH. Then the elements xHx_H form a basis of the AA-module C(Q)C(Q).

Bourbaki puts the proof directly after the statement, so what is above is the statement and its proof together.

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