algebraic integer

Noun

 * 1)  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 $$ z = a + i b $$ is an algebraic integer since it is a solution of either the equation $$ z^2 + (-2 a) z + (a^2 + b^2) = 0 $$ or the equation $$ z - a = 0 $$.
 * 1) * 1989, Heinrich Rolletschek, Shortest Division Chains in Imaginary Quadratic Number Fields, Patrizia Gianni (editor), Symbolic and Algebraic Computation: International Symposium, Springer, 358, page 231,
 * Let $$O_d$$ be the set of algebraic integers in an imaginary quadratic number field $$\Q[\sqrt{d}],\ d < 0$$, where $$d$$ is the discriminant of $$O_d$$.
 * Let $$O_d$$ be the set of algebraic integers in an imaginary quadratic number field $$\Q[\sqrt{d}],\ d < 0$$, where $$d$$ is the discriminant of $$O_d$$.

Translations

 * Chinese:
 * Mandarin: 代數整數
 * Finnish: algebrallinen kokonaisluku
 * French: entier algébrique
 * Greek: αλγεβρικός ακέραιος
 * Hungarian: algebrai egész
 * Italian: intero algebrico
 * Spanish: número entero algebraico
 * Swedish: