Ana Sayfa
Matematikçiler
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Matematik Seçkileri
Fraktallar
Paradokslar
Sayılar Teorisi
=> Algebraic Curves-Mordell Curve
=> Algebraic Curves-Ochoa Curve
=> Algebraic Integer
=> Algebraic Number
=> Algebraic Number Theory
=> Chebotarev Density Theorem
=> Class Field
=> Cyclotomic Field
=> Dedekind Ring
=> Fractional Ideal
=> Global Field
=> Local Field
=> Number Field Signature
=> Picard Group
=> Pisot Number
=> Weyl Sum
=> Casting Out Nines
=> A-Sequence
=> Anomalous Cancellation
=> Archimedes' Axiom
=> B2-Sequence
=> Calcus
=> Calkin-Wilf Tree
=> Egyptian Fraction
=> Egyptian Number
=> Erdős-Straus Conjecture
=> Erdős-Turán Conjecture
=> Eye of Horus Fraction
=> Farey Sequence
=> Ford Circle
=> Irreducible Fraction
=> Mediant
=> Minkowski's Question Mark Function
=> Pandigital Fraction
=> Reverse Polish Notation
=> Division by Zero
=> Infinite Product
=> Karatsuba Multiplication
=> Lattice Method
=> Pippenger Product
=> Reciprocal
=> Russian Multiplication
=> Solidus
=> Steffi Problem
=> Synthetic Division
=> Binary
=> Euler's Totient Rule
=> Goodstein Sequence
=> Hereditary Representation
=> Least Significant Bit
=> Midy's Theorem
=> Moser-de Bruijn Sequence
=> Negabinary
=> Negadecimal
=> Nialpdrome
=> Nonregular Number
=> Normal Number
=> One-Seventh Ellipse
=> Quaternary
=> Radix
=> Regular Number
=> Repeating Decimal
=> Saunders Graphic
=> Ternary
=> Unique Prime
=> Vigesimal
Ziyaretçi defteri
 

Algebraic Integer

If r is a root of the polynomial equation

 x^n+a_(n-1)x^(n-1)+...+a_1x+a_0=0,

where the a_is are integers and r satisfies no similar equation of degree <n, then r is called an algebraic integer of degree n. An algebraic integer is a special case of an algebraic number (for which the leading coefficient a_n 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 impossibility theorem shows that there are algebraic integers of degree >=5 which are not expressible in terms of addition, subtraction, multiplication, division, and root extraction (the elementary operations) on rational numbers. In fact, if elementary operations are allowed on real numbers only, then there are real numbers which are algebraic integers of degree 3 that cannot be so expressed.

The Gaussian integers are algebraic integers of Q(sqrt(-1)), since a+bi are roots of

 z^2-2az+a^2+b^2=0.
 

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