Ring of algebraic integers

In algebraic number theory, an algebraic integer is a complex number that is a root of some monic polynomial (a polynomial whose leading coefficient is 1) with coefficients in ${\displaystyle \mathbb {Z} }$ (the set of integers). The set of all algebraic integers, ${\displaystyle A}$, is closed under addition and multiplication and therefore is a commutative subring of the complex numbers. The ring ${\displaystyle A}$ is the integral closure of regular integers ${\displaystyle \mathbb {Z} }$ in complex numbers.

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