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Update rings.tex (#232)
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Small edit on requirements for a Euclidean Norm
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sphericalducky authored Apr 4, 2024
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Expand Up @@ -431,7 +431,7 @@ \section{Extra: Euclidean domains}
It's the absolute value $|\cdot|$ which is used to compare the magnitude of two numbers,
and this absolute value satisfies two conditions:
\begin{itemize}
\ii It takes nonnegative integer values --- that way, the algorithm will eventually terminate.
\ii It outputs nonnegative integer values --- that way, the algorithm will eventually terminate.
\ii For any two ring elements $a$ and $b$, where $b \neq 0$, there exist some $q$ such that
$r = a-qb$ has smaller absolute value than $b$.
\end{itemize}
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