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bobovski Permalink
January 22, 2010, 21:03

Nate, there is an algebraic structure on R^2 that behaves a lot like a vector space structure for which Z^2 *is* a sub-thingy. Instead of multiplying vectors in R^2 by real scalars, you allow only multiplication by integers. This gives R^2 the structure of a Z-module, and Z^2 is a submodule of R^2 with this structure.

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