Use this tag for questions related to numbers that are roots of a non-zero polynomial in one variable with rational coefficients.
An algebraic number is any complex number that is a root of a non-zero polynomial in one variable with rational coefficients or, equivalently by clearing denominators, with integer coefficients. The set of all algebraic numbers is usually denoted by $\mathbb A$.
All integers and rational numbers are algebraic as are all roots of integers (including $\pm i$). The same is not true for all real and complex numbers because they also include transcendental numbers such as $\pi$ and $e$.
If $a$ and $b$ are algebraic numbers, then so are the numbers $a+b$, $-a$, $ab$ and (if $a\neq0$) $1/a$. Therefore, $\mathbb A$ is a field.
