10 lines
399 B
TeX
10 lines
399 B
TeX
\section{Subrings}
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\begin{definition}[Subring]
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A subset $S$ of a ring $R$ is a \textit{subring of $R$} if $S$ is itself a ring with the operations of $R$.
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\end{definition}
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\begin{theorem}[Subring Test]
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A nonempty subset $S$ of a ring $R$ is a subring if $S$ is closed under subtraction and multiplication -- that is, if $a - b$ and $ab$ are in $S$ whenever $a$ and $b$ are in $S$.
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\end{theorem}
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