14 lines
396 B
TeX
14 lines
396 B
TeX
\section{Fields}
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\begin{definition}[Field]
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A \textit{field} is a commutative ring with unity in which every nonzero element is a unit.
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\end{definition}
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\begin{theorem}[Finite Integral Domains are Fields]
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A finite integral domain is a field.
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\end{theorem}
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\begin{corollary}[$\mathbf{\Z_p}$ Is a Field]
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For every prime $p$, $\Z_p$, the ring of integers modulo $p$ is a field.
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\end{corollary}
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