16D40-AbsolutelyFlat.tex

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\begin{document}
A ring $A$ is \emph{absolutely flat} if every module over $A$ is flat.

For commutative rings with unity, a ring is absolutely flat if and only if every principal ideal is idempotent.

Some properties:

\begin{itemize}
\item Boolean rings are flat.
\item Homomorphic images of absolutely flat rings are flat.
\item Absolutely flat local rings are fields.
\item In absolutely flat rings, non-units are zero divisors.
\end{itemize}


\begin{thebibliography}{9}
\bibitem {AtMac} \emph{Introduction to \PMlinkescapetext{Commutative Algebra}}, by Atiyah and MacDonald.
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