## Infinite Integer Product Not Free

Introduction Assuming the axiom of choice, any vector space possesses the pleasant but prosaic property* that it is determined up to isomorphism by the cardinality of its basis. For instance, consider $ \prod_\omega \mathbb{Z}/2$ and $ \oplus_{2^\omega} \mathbb{Z}/2$. Both are vector spaces over the finite field $ \mathbb{Z}/2$ so to show that they are isomorphic, […]