Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Subrings}
+
+\begin{definition}[Subring]
+	A subset $S$ of a ring $R$ is a \textit{subring of $R$} if $S$ is itself a ring with the operations of $R$.
+\end{definition}
+
+\begin{theorem}[Subring Test]
+	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 $S$.
+\end{theorem}