division ring
DivisionRing
2001-10-19 00:30:52
2006-10-22 01:44:22
Definition
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A \emph{division ring} is a ring $D$ with identity such that
\begin{itemize}
\item $1 \neq 0$
\item For all nonzero $a \in D$, there exists $b \in D$ with $a \cdot b = b \cdot a = 1$
\end{itemize}
Every field is a commutative division ring. The Hamiltonian quaternions are an example of a division ring which is not a field.