Field (mathematics)

In mathematics a field is a certain kind of algebraic structure. In a field you can add ($x+y$), subtract ($x-y$), multiply ($x\cdot y$) and divide ($x/y$) two numbers (with division only allowed if $y$ is not equal to zero). A field is a special ring, in which you can divide.

Examples for fields are the real numbers $\mathbb{R}$ and the rational numbers $\mathbb{Q}$. The integers $\mathbb{Z}$ are not a field, because you cannot always divide without a remainder.