The Stacks project

Eilenberg swindle

[Eilenberg's lemma, Bass]

In [Bass] we find: “...is an elegant little swindle, observed several years ago by Eilenberg, and which might well have sprung from the brow of Barry Mazur.”

Proof.

\[ F \cong F \oplus F \oplus \ldots \cong P \oplus Q \oplus P \oplus Q \oplus \ldots \cong P \oplus F \oplus F \oplus \ldots \cong P \oplus F \]
$\square$

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View Lemma 15.128.1 as pdf