Ring of integers in a number field - Revision history

Vipul: 3 revisions

2008-05-12T16:34:33Z

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Vipul at 18:32, 17 December 2007

2007-12-17T18:32:43Z

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			{{redirect\|ring of integers\|the ring of rational integers\|ring of rational integers}}

	==Definition==		==Definition==

Vipul at 18:11, 17 December 2007

2007-12-17T18:11:11Z

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	The ring of integers in a number field is also termed a '''maximal order''', here an [[order in a number field\|order]] is a subring of <math>K</math> which is free as a <math>\mathbb{Z}</math>-module, and which, over <math>\mathbb{Q}</math>, generates <math>K</math>.		The ring of integers in a number field is also termed a '''maximal order''', here an [[order in a number field\|order]] is a subring of <math>K</math> which is free as a <math>\mathbb{Z}</math>-module, and which, over <math>\mathbb{Q}</math>, generates <math>K</math>.

			==Relation with other properties==

			===Weaker properties===

			* [[Dedekind domain]]

Vipul at 18:10, 17 December 2007

2007-12-17T18:10:32Z

New page

{{curing property}}

==Definition==

Let <math>K</math> be a [[number field]]. Then the '''ring of integers''' in <math>K</math>, denoted <math>O_K</math>, is the subring of <math>K</math> comprising all those elements which are integral over <math>\mathbb{Z}</math>, in other words, which satisfy monic polynomials with integer coefficients.

The ring of integers in a number field is also termed a '''maximal order''', here an [[order in a number field|order]] is a subring of <math>K</math> which is free as a <math>\mathbb{Z}</math>-module, and which, over <math>\mathbb{Q}</math>, generates <math>K</math>.