# Difference between revisions of "Ring of integers"

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− | Let <math>K</math> be | + | Let <math>K</math> be a finite [[algebraic]] [[field extension]] of <math>\mathbb{Q}</math>. Then the [[integral closure]] of <math>{\mathbb{Z}}</math> in <math>K</math>, which we denote by <math>\mathfrak{o}_K</math>, is called the '''ring of integers''' of <math>K</math>. Rings of integers are always [[Dedekind domain]]s with finite [[class number]]s. |

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## Revision as of 13:30, 10 December 2007

Let be a finite algebraic field extension of . Then the integral closure of in , which we denote by , is called the **ring of integers** of . Rings of integers are always Dedekind domains with finite class numbers.

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