Exercise 14, § 11

Tag 00E5, permanent. Cite it as [Bourbaki, Tag 00E5].

Algebra, VIII, p. 210

Let K be a commutative field of characteristic different from 2. Write

A = K[X,Y,Z]/(X^2+ Y^2+ Z^2-1)

Let M be the A-module $A^3/A(X,\overline{Y},Z)$ , where X, Y, and $\overline{Z}$ denote the respective images of X, Y, and Z in A. Show that $M\oplus A$ is a free A-module but that M is not a free module.

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Cited by

§ 11. Grothendieck Groups

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