Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Factor Rings}
+
+\begin{theorem}[Existence of Factor Rings]
+	Let $R$ be a ring and let $A$ be a subring of $R$. The set of cosets $\{r + A\ \vert\ r \in R\}$ is a ring under the operations $(s + A) + (t + A) = s + t + A$ and $(s+A)(t+A)=st+A$ if and only if $A$ is an ideal of $R$.
+\end{theorem}