Algebraic Integers

An algebraic integer is a complex number that is the solution to an algebraic equation having leading coefficient 1, meaning that the coefficient of the highest power of \(x\) is 1. For example the equation \(x^2 = 2\) has leading coefficient 1, and its solutions, namely the square root of 2, and minus the square root of 2, are algebraic integers. On the other hand, the equation \(2x = 1\) has leading coefficient 2, and its solution, \(x = 1/2\), is not an algebraic integer. An algebraic integer that is a rational number must be an ordinary integer.

The entries in a character table are algebraic integers.