AlgebraicIntegerQ

AlgebraicIntegerQ[a] yields True if a is an algebraic integer, and yields False otherwise.

Examples

Test if a number is an algebraic integer:

AlgebraicIntegerQ[Sqrt[2]]
(* True *)

Rational numbers that aren't integers are not algebraic integers:

AlgebraicIntegerQ[1/2]
(* False *)

Please visit the official Wolfram Language Reference for more details.