From Milnor's book "Algebraic K-Theory":
A (nonzero!) associative ring for which a free module of rank 2 is isomorphic to a free module of rank 1: The ring of endomorphisms of an infinite-dimensional vector space.
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A (nonzero!) associative ring for which a free module of rank 2 is isomorphic to a free module of rank 1: The ring of endomorphisms of an infinite-dimensional vector space. |
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