Usually means: Root of monic polynomial with integers.
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We found 5 dictionaries that define the word algebraic integer:

General (2 matching dictionaries)
  1. algebraic integer: Wiktionary
  2. Algebraic integer: Wikipedia, the Free Encyclopedia

Computing (1 matching dictionary)
  1. algebraic integer: Encyclopedia

Science (2 matching dictionaries)
  1. Algebraic Integer: Eric Weisstein's World of Mathematics
  2. algebraic integer: PlanetMath Encyclopedia

Definitions from Wiktionary (algebraic integer)

noun:  (algebra, number theory) 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.

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