Created the Abstract Algebra theorems and definitions cheat sheet

part-3/chapters/chapter-14/ideals.tex

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+\section{Ideals}
+
+\begin{definition}[Ideal]
+	A subring $A$ of a ring $R$ is called a (two-sided) \textit{ideal} of $R$ if for every $r \in R$ and every $a \in A$ both $ra$ and $ar$ are in $A$.
+\end{definition}
+
+\begin{theorem}[Ideal Test]
+	A nonempty subset $A$ of a ring $R$ is an ideal of $R$ if
+	\begin{enumerate}
+		\item $a-b \in A$ whenever $a,b \in A$.
+		\item $ra$ and $ar$ are in $A$ whenever $a \in A$ and $r \in R$.
+	\end{enumerate}
+\end{theorem}