# Divided domain

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In algebra, a divided domain is an integral domain R in which every prime ideal ${\displaystyle {\mathfrak {p}}}$ satisfies ${\displaystyle {\mathfrak {p}}={\mathfrak {p}}R_{\mathfrak {p}}}$. A locally divided domain is an integral domain that is a divided domain at every maximal ideal. A Prüfer domain is a basic example of a locally divided domain.[1] Divided domains were introduced by Akiba (1967) who called them AV-domains.

## References

1. ^ http://downloads.hindawi.com/journals/ijmms/1981/108278.pdf
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