A few years ago I gave a departmental colloquium talk, aimed at beginning M.A. students, on "An application of calculus to ring theory." A slightly facetious little abstract can be found here. The example establishing the main resultsvery well known to workers in commutative ring theorywas the ring of germs at $0$ of class $C^{\infty}$ functions on $\mathbb{R}$. A bit of calculus is needed in verifying the requisite properties.
Greg Marks
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