Difference between revisions of "Ring of integers"

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Let <math>K</math> be an [[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.
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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 $K$ be a finite algebraic field extension of $\mathbb{Q}$. Then the integral closure of ${\mathbb{Z}}$ in $K$, which we denote by $\mathfrak{o}_K$, is called the ring of integers of $K$. Rings of integers are always Dedekind domains with finite class numbers.

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