algebraic integer

Let $K$ be an extension (http://planetmath.org/ExtensionField) of $\mathbb{Q}$ contained in $ℂ$. A number $\alpha \in K$ is called an algebraic integer of $K$ if it is the root of a monic polynomial with coefficients in $\mathbb{Z}$, i.e., an element of $K$ that is integral over $\mathbb{Z}$. Every algebraic integer is an algebraic number (with $K=ℂ$), but the converse is false.

Title	algebraic integer
Canonical name	AlgebraicInteger
Date of creation	2013-03-22 11:45:41
Last modified on	2013-03-22 11:45:41
Owner	KimJ (5)
Last modified by	KimJ (5)
Numerical id	13
Author	KimJ (5)
Entry type	Definition
Classification	msc 11R04
Classification	msc 62-01
Classification	msc 03-01
Related topic	IntegralBasis
Related topic	CyclotomicUnitsAreAlgebraicUnits
Related topic	FundamentalUnits
Related topic	Monic2
Related topic	RingWithoutIrreducibles