6 lines
303 B
TeX
6 lines
303 B
TeX
\section{Factor Rings}
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\begin{theorem}[Existence of Factor Rings]
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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 $R$.
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\end{theorem}
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