Algebraic integer Guide, Meaning , Facts, Information and Description

In mathematics, an algebraic integer is a complex number α that is a root of an equation

P(x) = 0

where the coefficients of the polynomial P(x) are integers and P is monic (i.e. the coefficient of the top term x is 1).

The algebraic integers are all therefore algebraic numbers, but not all algebraic numbers are algebraic integers.

The sum of two algebraic integers is an algebraic integer, and so is their difference; their product is too, but not necessarily their ratio. An integer root of an algebraic integer is also an algebraic integer. So all radical integers are algebraic integers but not all algebraic integers are radical integers.

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