Difference between revisions of "Ring of integers"

Revision as of 14:30, 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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Revision as of 18:19, 12 July 2006 (view source) ComplexZeta (talk \| contribs) ← Older edit		Revision as of 14:30, 10 December 2007 (view source) ZetaX (talk \| contribs) Newer edit →
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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.	+	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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