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quotient rings in algebraic geometry. As a simple case, consider the real variety as a subset of the real plane . The ring of real-valued polynomial functions defined on can be identified with the quotient ring , and this is the coordinate ring of . The variety is now investigated by studying its coordinate ring.
* Suppose is a -manifold, and is a point of . Consider the ring of all -functions defined on and let be the ideal in consisting of those functions

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