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Revision difference : division ring |
| Version 2 |
Version 1 |
| A {\em division ring} is a ring $D$ with identity such that |
A {\em division ring} is a ring $D$ with identity such that |
| \begin{itemize} |
\begin{itemize} |
| \item $1 \neq 0$ |
\item $1 \neq 0$ |
| \item For all $a \in D$, there exists $b \in D$ with $a \cdot b = b \cdot a = 1$ |
\item For all $a \in D$, there exists $b \in D$ with $a \cdot b = b \cdot a = 1$ |
| \end{itemize} |
\end{itemize} |
| A field is equivalent to a commutative division ring. |
A field is equivalent to a commutative division ring. |
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