8 lines
458 B
TeX
8 lines
458 B
TeX
\section{Definition and Examples}
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\begin{definition}[Ring Homomorphism, Ring Isomorphism]
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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 $R$,
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\[ \phi(a + b) = \phi(a) + \phi(b)\ \ \ \ \text{and}\ \ \ \ \phi(ab) = \phi(a)\phi(b) \]
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A ring homomorphism that is both one-to-one and onto is called a \textit{ring isomorphism}.
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\end{definition}
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