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. | + | 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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Revision as of 17:19, 12 July 2006
Let 
be an 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.
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