Algebraic Integer
If 
is a Root of the Polynomial equation
where the
s are Integers and satisfies no similar equation of degree 
, then is analgebraic Integer of degree 
. An algebraic Integer is a special case of an Algebraic Number, forwhich the leading Coefficient 
need not equal 1. Radical Integers are a subring of the Algebraic Integers. A Sum or Product of algebraic integers is again an algebraic integer. However, Abel's ImpossibilityTheorem shows that there are algebraic integers of degree 
which are not expressible in terms of Addition,Subtraction, Multiplication, Division, and the extraction of Roots onReal Numbers.
The Gaussian Integers are algebraic integers of 
, since 
are roots of
See also Algebraic Number, Euclidean Number, Radical Integer
References
Hancock, H. Foundations of the Theory of Algebraic Numbers, Vol. 1: Introduction to the General Theory. New York: Macmillan, 1931. Hancock, H. Foundations of the Theory of Algebraic Numbers, Vol. 2: The General Theory. New York: Macmillan, 1932. Pohst, M. and Zassenhaus, H. Algorithmic Algebraic Number Theory. Cambridge, England: Cambridge University Press, 1989. Wagon, S. ``Algebraic Numbers.'' §10.5 in Mathematica in Action. New York: W. H. Freeman, pp. 347-353, 1991.
- Noetherian Module
- Noetherian Ring
- Noether-Lasker Theorem
- Noether's Fundamental Theorem
- Noether's Transformation Theorem
- Noise
- Noise Sphere
- Nolid
- Nome
- n-Omino
- Nomogram
- Nonagon
- Nonagonal Number
- Nonagram
- Nonassociative Algebra
- Nonassociative Product
- Nonaveraging Sequence
- Noncentral Distribution
- Noncommutative Group
- Nonconformal Mapping
- Nonconstructive Proof
- Noncototient
- Noncylindrical Ruled Surface
- Nondecreasing Function
- Nondividing Set