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Quotient Ring

The quotient ring of $R$ with respect to a Ring modulo some Integer $n$ is denoted $R/nR$ and is read ``the ring $R$ modulo $n$.'' If $n$ is a Prime $p$, then $\Bbb{Z}/p\Bbb{Z}$ is the Finite Field $\Bbb{F}_p$. For Composite

\begin{displaymath}
n=\prod_{i=1}^k p_i
\end{displaymath}

with distinct $p_i$, $\Bbb{Z}/n\Bbb{Z}$ is Isomorphic to the Direct Sum

\begin{displaymath}
\Bbb{Z}/n\Bbb{Z} = \Bbb{F}_{p_1}\otimes\Bbb{F}_{p_2}\otimes\cdots\otimes\Bbb{F}_{p_k}.
\end{displaymath}

See also Finite Field, Ring




© 1996-9 Eric W. Weisstein
1999-05-25