Algebraic integer

English

Noun

1. Template:Lb A real or complex number (more generally, an element of a number field) which is a root of a monic polynomial whose coefficients are integers; equivalently, an algebraic number whose minimal polynomial (lowest-degree polynomial of which it is a root and whose leading coefficient is 1) has integer coefficients.

   A Gaussian integer $z=a+ib$ is an algebraic integer since it is a solution of either the equation $z^2+(-2a)z+(a^2+b^2)=0$ or the equation $z-a=0$.

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   • 1989, Heinrich Rolletschek, Shortest Division Chains in Imaginary Quadratic Number Fields, Patrizia Gianni (editor), Symbolic and Algebraic Computation: International Symposium, Springer, Template:W 358, page 231,

     Let $O_d$ be the set of algebraic integers in an imaginary quadratic number field $\mathbb{Q}[\sqrt{d}],d<0$, where $d$ is the discriminant of $O_d$.

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• algebraic integer on Template:W
• Algebraic Integer on Template:W