In algebraic number theory, an algebraic integer is a complex number which is integral over the integers. Wikipedia

Complex number that solves a monic polynomial with integer coefficients Wikidata

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. Wiktionary

Algebraic number whose minimal polynomial has integer coefficients. Wiktionary (translation)