Field (mathematics)

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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 of fields

Examples for fields are

• the real numbers $\mathbb{R}$
• the rational numbers $\mathbb{Q}$
• the complex numbers $\mathbb{C}$

The integers $\mathbb{Z}$ are not a field, because you cannot always divide without a remainder.