Difference between revisions of "Ring of integers"

Latest revision as of 17:36, 28 September 2024

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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-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.
 {{stub}}
+[[Category:Definition]]
+[[Category:Field theory]]
+[[Category:Ring theory]]
+[[Category:Mathematics]]
+[[category:Abstract algebra]]