Created the Abstract Algebra theorems and definitions cheat sheet

2024-01-09 11:30:56 -07:00
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+\section{Definition and Examples}
+
+\begin{definition}[Ring Homomorphism, Ring Isomorphism]
+	A \textit{ring homomorphism} $\phi$ from a ring $R$ to a ring $S$ is a mapping from $R$ to $S$ that preserves the two ring operations; that is, for all $a,b$ in $R$,
+	\[ \phi(a + b) = \phi(a) + \phi(b)\ \ \ \ \text{and}\ \ \ \ \phi(ab) = \phi(a)\phi(b) \]
+	A ring homomorphism that is both one-to-one and onto is called a \textit{ring isomorphism}.
+\end{definition}