LYCOS RETRIEVER 
Algebraic Number
built 806 days ago
An algebraic integer is a number which is a root of a polynomial with integer coefficients (that is, an algebraic number) with leading coefficient 1 (a monic polynomial). Examples of algebraic integers are 3√
Source:
![[Schematic of subareas and related areas]](http://retrieverimages.lycos.com/images/a/l/g/algebraic-number/i/000.gif)
The sets of solutions in rational numbers to algebraic equations may be viewed as algebraic varieties, and ... studied with tools of 14: Algebraic Geometry. This is particularly true with single equations in two variables (which lead to curves); such equations when of degree 3 (or 4) lead to elliptic curves.
Source:
Some irrational numbers are algebraic though. For example, all square roots (for example, 2 satisfy quadratic equations, and other roots satisfy other equations of higher degree. On the other hand, numbers such as log 2 and π are transcendental.
Source:
For algebraic numbers such a unique factorization need not hold. E.g. consider the field . In it, the number 6 has two essentially different factorizations: , . For extensions of higher degree the situation becomes still more complicated. The question arises: What becomes of the unique factorization theorem, does it have a meaning at all in algebraic number fields?
Source:
MORE ABOUT
Algebraic Number