Definition 15.3.1. Let $R$ be a ring.

Two modules $M$, $N$ over $R$ are said to be

*stably isomorphic*if there exist $n, m \geq 0$ such that $M \oplus R^{\oplus m} \cong N \oplus R^{\oplus n}$ as $R$-modules.A module $M$ is

*stably free*if it is stably isomorphic to a free module.

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