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| | Discrete valuation - Wikipedia, the free encyclopedia |
 | | In mathematics, a discrete valuation on an integral domain A is a function |
 | | Conversely, if B is the set of all elements in A with nonnegative valuation, then B is a subring of A, and the set of all elements in A with strictly positive valuation is a prime ideal of B. |
 | | For example, if K is a field, then the ring of power series over K in two unknowns, K[[X, Y]], has a discrete valuation induced by the prime ideal (X, Y), and is even local, but is not a discrete valuation ring because it's not a principal ideal domain. |
| en.wikipedia.org /wiki/Discrete_valuation (219 words) |
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