Editing Algebraic integer (section)

==Non-example==
* If {{math|''P''(''x'')}} is a [[Primitive polynomial (ring theory)|primitive polynomial]] that has integer coefficients but is not monic, and {{mvar|P}} is [[irreducible polynomial|irreducible]] over <math>\mathbb{Q}</math>, then none of the roots of {{mvar|P}} are algebraic integers (but ''are'' [[algebraic number]]s). Here ''primitive'' is used in the sense that the [[highest common factor]] of the coefficients of {{mvar|P}} is 1, which is weaker than requiring the coefficients to be pairwise relatively prime.