Example 9.3.2 (Prime fields). If $p$ is a prime number, then $\mathbf{Z}/(p)$ is a field, denoted $\mathbf{F}_ p$. Indeed, $(p)$ is a maximal ideal in $\mathbf{Z}$. Thus, fields may be finite: $\mathbf{F}_ p$ contains $p$ elements.

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