Lemma 15.128.1 (Eilenberg's lemma). If $P \oplus Q \cong F$ with $F$ a nonfinitely generated free module, then $P \oplus F \cong F$.
[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.”
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